Several recent works have focused on carrying out non-asymptotic convergence analyses for AC algorithms. Recently, a two-timescale critic-actor algorithm has been presented for the discounted cost setting in the look-up table case where the timescales of the actor and the critic are reversed and only asymptotic convergence shown. In our work, we present the first two-timescale critic-actor algorithm with function approximation in the long-run average reward setting and present the first finite-time non-asymptotic as well as asymptotic convergence analysis for such a scheme. We obtain optimal learning rates and prove that our algorithm achieves a sample complexity that can be made arbitrarily close to that of single-timescale AC and clearly better than the one obtained for two-timescale AC in a similar setting.. A notable feature of our analysis is that we present the asymptotic convergence analysis of our scheme in addition to the finite-time bounds that we obtain and show the almost sure asymptotic convergence of the (slower) critic recursion to the attractor of an associated differential inclusion with actor parameters corresponding to local maxima of a perturbed average reward objective. We also show the results of numerical experiments on three benchmark settings and observe that our critic-actor algorithm performs the best amongst all algorithms.

We propose a training-free method for feature field rendering in 3D Gaussian Splatting, enabling fast and scalable embedding of high-dimensional features into 3D scenes. Unlike training-based feature distillation methods, which are computationally expensive and often yield feature embeddings that poorly reflect the rendered semantics, our approach back-projects 2D features onto pre-trained 3D Gaussians using influence weights derived from the rendering equation. This projection produces a queryable 3D feature field, validated on tasks including 2D and 3D segmentation, affordance transfer, and identity encoding, spanning queries using language, pixel, and synthetic embeddings. These capabilities, in turn, enable downstream applications in augmented and virtual reality, interactive scene editing, and robotics. Across different tasks, our method achieves performance comparable to or better than training-based approaches, while significantly reducing computational cost. The project page is at https://jojijoseph.github.io/3dgs-backprojection.

We consider the problem of control in the setting of reinforcement learning (RL), where model information is not available. Policy gradient algorithms are a popular solution approach for this problem and are usually shown to converge to a stationary point of the value function. In this paper, we propose two policy Newton algorithms that incorporate cubic regularization. Both algorithms employ the likelihood ratio method to form estimates of the gradient and Hessian of the value function using sample trajectories. The first algorithm requires an exact solution of the cubic regularized problem in each iteration, while the second algorithm employs an efficient gradient descent-based approximation to the cubic regularized problem. We establish convergence of our proposed algorithms to a second-order stationary point (SOSP) of the value function, which results in the avoidance of traps in the form of saddle points. In particular, the sample complexity of our algorithms to find an $\epsilon$-SOSP is $O(\epsilon^{-3.5})$, which is an improvement over the state-of-the-art sample complexity of $O(\epsilon^{-4.5})$.

Actor Critic methods have found immense applications on a wide range of Reinforcement Learning tasks especially when the state-action space is large. In this paper, we consider actor critic and natural actor critic algorithms with function approximation for constrained Markov decision processes (C-MDP) involving inequality constraints and carry out a non-asymptotic analysis for both of these algorithms in a non-i.i.d (Markovian) setting. We consider the long-run average cost criterion where both the objective and the constraint functions are suitable policy-dependent long-run averages of certain prescribed cost functions. We handle the inequality constraints using the Lagrange multiplier method. We prove that these algorithms are guaranteed to find a first-order stationary point (i.e., $\Vert \nabla L(\theta,\gamma)\Vert_2^2 \leq \epsilon$) of the performance (Lagrange) function $L(\theta,\gamma)$, with a sample complexity of $\mathcal{\tilde{O}}(\epsilon^{-2.5})$ in the case of both Constrained Actor Critic (C-AC) and Constrained Natural Actor Critic (C-NAC) algorithms. We also show the results of experiments on three different Safety-Gym environments.

The average reward criterion is relatively less studied as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this work, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We first show asymptotic convergence analysis using the ODE-based method. Subsequently, we provide a finite time analysis of the resulting stochastic approximation scheme with linear function approximator and obtain an $\epsilon$-optimal stationary policy with a sample complexity of $\Omega(\epsilon^{-2.5})$. We compare the average reward performance of our proposed ARO-DDPG algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo-based environments.

Autonomous navigation of Unmanned Aerial Vehicles (UAVs) has real-life applications in remote sensing, wildlife surveillance, search and rescue operations. A popular training paradigm to learn optimal actions for navigating such complex, dynamic, and uncertain environments is Reinforcement Learning (RL), where the optimal decisions are learnt over time through a reward-feedback received from the environment. However, manually constructing a feedback function that can help guide the UAV to accomplish the desired objective is often very hard. Preference-based Reinforcement Learning (PbRL) is an emerging sub-field of RL where the manual construction of reward function is replaced with human feedback. In this setting, a human is presented with a pair of trajectories followed by the RL agent to elicit the subject’s preference for one over the other. A PbRL algorithm would then compute an optimal sequence of actions using just the set of preferences collected over different trajectories. In this work, we consider PbRL for UAV navigation and follow an ensemble approach to enhance navigation performance. We demonstrate the efficacy of the proposed algorithm through experiments on a range of complex environments and tasks. Ours is the first work that uses human preferences to solve the UAV navigation problem to the best of our knowledge.

Gradient temporal difference (Gradient TD) algorithms are a popular class of stochastic approximation (SA) algorithms used for policy evaluation in reinforcement learning. Here, we consider Gradient TD algorithms with an additional heavy ball momentum term and provide choice of step size and momentum parameter that ensures almost sure convergence of these algorithms asymptotically. In doing so, we decompose the heavy ball Gradient TD iterates into three separate iterates with different step sizes. We first analyze these iterates under one-timescale SA setting using results from current literature. However, the one-timescale case is restrictive and a more general analysis can be provided by looking at a three-timescale decomposition of the iterates. In the process we provide the first conditions for stability and convergence of general three-timescale SA. We then prove that the heavy ball Gradient TD algorithm is convergent using our three-timescale SA analysis. Finally, we evaluate these algorithms on standard RL problems and report improvement in performance over the vanilla algorithms.

Recent works in Reinforcement Learning (RL) combine model-free (Mf)-RL algorithms with model-based (Mb)-RL approaches to get the best from both: asymptotic performance of Mf-RL and high sample-efficiency of Mb-RL. Inspired by these works, we propose a hierarchical framework that integrates online learning for the Mb-trajectory optimization with off-policy methods for the Mf-RL. In particular, two loops are proposed, where the Dynamic Mirror Descent based Model Predictive Control (DMD-MPC) is used as the inner loop Mb-RL to obtain an optimal sequence of actions. These actions are in turn used to significantly accelerate the outer loop Mf-RL. We show that our formulation is generic for a broad class of MPC based policies and objectives, and includes some of the well-known Mb-Mf approaches. We finally introduce a new algorithm: Mirror-Descent Model Predictive RL (M-DeMoRL), which uses Cross-Entropy Method (CEM) with elite fractions for the inner loop. Our experiments show faster convergence of the proposed hierarchical approach on benchmark MuJoCo tasks. We also demonstrate hardware training for trajectory tracking in a 2R leg, and hardware transfer for robust walking in a quadruped. We show that the inner-loop Mb-RL significantly decreases the number of training iterations required in the hardware setting, thereby validating the proposed approach.

Learning optimal behavior from existing data is one of the most important problems in Reinforcement Learning (RL). This is known as “off-policy control” in RL where an agent's objective is to compute an optimal policy based on the data obtained from the given policy (known as the behavior policy). As the optimal policy can be very different from the behavior policy, learning optimal behavior is very hard in the “off-policy” setting compared to the “on-policy” setting where new data from the policy updates is typically utilized in learning. This work proposes an off-policy natural actor-critic algorithm that utilizes state-action distribution correction for handling the off-policy behavior and the natural policy gradient for sample efficiency. The existing natural gradient-based actor-critic algorithms with convergence guarantees require fixed features for approximating both policy and value functions. This often leads to sub-optimal learning in many RL applications. On the other hand, our proposed algorithm utilizes compatible features that enable one to use arbitrary neural networks to approximate the policy and the value function and yet guarantee convergence to a locally optimal policy. We illustrate the benefit of the proposed off-policy natural gradient algorithm by comparing it with the vanilla gradient actor-critic algorithm on benchmark RL tasks.

During initial iterations of training in most Reinforcement Learning (RL) algorithms, agents perform a significant number of random exploratory steps. In the real world, this can limit the practicality of these algorithms as it can lead to potentially dangerous behavior. Hence safe exploration is a critical issue in applying RL algorithms in the real world. This problem has been recently well studied under the Constrained Markov Decision Process (CMDP) Framework, where in addition to single-stage rewards, an agent receives single-stage costs or penalties as well depending on the state transitions. The prescribed cost functions are responsible for mapping undesirable behavior at any given time-step to a scalar value. The goal then is to find a feasible policy that maximizes reward returns while constraining the cost returns to be below a prescribed threshold during training as well as deployment.We propose an On-policy Model-based Safe Deep RL algorithm in which we learn the transition dynamics of the environment in an online manner as well as find a feasible optimal policy using the Lagrangian Relaxation-based Proximal Policy Optimization. We use an ensemble of neural networks with different initializations to tackle epistemic and aleatoric uncertainty issues faced during environment model learning. We compare our approach with relevant model-free and model-based approaches in Constrained RL using the challenging Safe Reinforcement Learning benchmark - the Open AI Safety Gym. We demonstrate that our algorithm is more sample efficient and results in lower cumulative hazard violations as compared to constrained model-free approaches. Further, our approach shows better reward performance than other constrained model-based approaches in the literature.

Applying reinforcement learning (RL) methods for real world applications pose multiple challenges - the foremost being safety of the system controlled by the learning agent and the learning efficiency. An RL agent learns to control a system by exploring the available actions in various operating states. In some states, when the RL agent exercises an exploratory action, the system may enter unsafe operation, which can lead to safety hazards both for the system as well as for humans supervising the system. RL algorithms thus must learn to control the system respecting safety. In this work, we formulate the safe RL problem in the constrained off-policy setting that facilitates safe exploration by the RL agent. We then develop a sample efficient algorithm utilizing the cross-entropy method. The proposed algorithm’s safety performance is evaluated numerically on benchmark RL problems.

This paper presents our method for enabling a UAV quadrotor, equipped with a monocular camera, to autonomously avoid collisions with obstacles in unstructured and unknown indoor environments. When compared to obstacle avoidance in ground vehicular robots, UAV navigation brings in additional challenges because the UAV motion is no more constrained to a well-defined indoor ground or street environment. Unlike ground vehicular robots, a UAV has to navigate across more types of obstacles - for e.g., objects like decorative items, furnishings, ceiling fans, sign-boards, tree branches, etc., are also potential obstacles for a UAV. Thus, methods of obstacle avoidance developed for ground robots are clearly inadequate for UAV navigation. Current control methods using monocular images for UAV obstacle avoidance are heavily dependent on environment information. These controllers do not fully retain and utilize the extensively available information about the ambient environment for decision making. We propose a deep reinforcement learning based method for UAV obstacle avoidance (OA) which is capable of doing exactly the same. The crucial idea in our method is the concept of partial observability and how UAVs can retain relevant information about the environment structure to make better future navigation decisions. Our OA technique uses recurrent neural networks with temporal attention and provides better results compared to prior works in terms of distance covered without collisions. In addition, our technique has a high inference rate and reduces power wastage as it minimizes oscillatory motion of UAV.

Option-critic learning is a general-purpose reinforcement learning (RL) framework that aims to address the issue of long term credit assignment by leveraging temporal abstractions. However, when dealing with extended timescales, discounting future rewards can lead to incorrect credit assignments. In this work, we address this issue by extending the hierarchical option-critic policy gradient theorem for the average reward criterion. Our proposed framework aims to maximize the long-term reward obtained in the steady-state of the Markov chain defined by the agent's policy. Furthermore, we use an ordinary differential equation based approach for our convergence analysis and prove that the parameters of the intra-option policies, termination functions, and value functions, converge to their corresponding optimal values, with probability one. Finally, we illustrate the competitive advantage of learning options, in the average reward setting, on a grid-world environment with sparse rewards.

Learning the value function of a given policy (target policy) from the data samples obtained from a different policy (behavior policy) is an important problem in Reinforcement Learning (RL). This problem is studied under the setting of off-policy prediction. Temporal Difference (TD) learning algorithms are a popular class of algorithms for solving the prediction problem. TD algorithms with linear function approximation are shown to be convergent when the samples are generated from the target policy (known as on-policy prediction). However, it has been well established in the literature that off-policy TD algorithms under linear function approximation diverge. In this work, we propose a convergent on-line off-policy TD algorithm under linear function approximation. The main idea is to penalize the updates of the algorithm in a way as to ensure convergence of the iterates. We provide a convergence analysis of our algorithm. Through numerical evaluations, we further demonstrate the effectiveness of our algorithm.

We present a new deep reinforcement learning algorithm using the technique of successive over-relaxation (SOR) in Deep Q-networks (DQNs). The new algorithm, named SOR-DQN, uses modified targets in the DQN framework with the aim of accelerating training. This work is motivated by the problem of auto-scaling resources for cloud applications, for which existing algorithms suffer from issues such as slow convergence, poor performance during the training phase and non-scalability. For the above problem, SOR-DQN achieves significant improvements over DQN on both synthetic and real datasets. We also study the generalization ability of the algorithm to multiple tasks by using it to train agents playing Atari video games.

We consider an industrial internet-of-things (IIoT) system with multiple IoT devices, a user equipment (UE), together with a base station (BS) that receives the UE and IoT data. To circumvent the issue of numerous IoT-to-BS connections and to conserve IoT devices' energies, the UE serves as a relay to forward the IoT data to the BS. The UE employs frame-based uplink transmissions, wherein it shares few slots of every frame to relay the IoT data. The IIoT system experiences a transmission failure called outage when IoT data is not transmitted. The unsent UE data is stored in the UE's buffer and is discarded after the storage time exceeds the age threshold. As the UE and IoT devices share the transmission slots, trade-offs exist between system outages and aged UE data loss. To resolve system outage-data ageing challenge, we provide model-free reinforcement learning (RL)-based policies for slot-sharing between UE and IoT data. We compare the performance of the RL-based policies with low complexity heuristic-based slot-sharing schemes which either prioritise the UE data or account only for near-threshold aged UE data or are oblivious to the amount of UE data.

With the research into development of quadruped robots picking up pace, learning based techniques are being explored for developing locomotion controllers for such robots. A key problem is to generate leg trajectories for continuously varying target linear and angular velocities, in a stable manner. In this paper, we propose a two pronged approach to address this problem. First, multiple simpler policies are trained to generate trajectories for a discrete set of target velocities and turning radius. These policies are then augmented using a higher level neural network for handling the transition between the learned trajectories. Specifically, we develop a neural network based filter that takes in target velocity, radius and transforms them into new commands that enable smooth transitions to the new trajectory. This transformation is achieved by learning from expert demonstrations. An application of this is the transformation of a novice user's input into an expert user's input, thereby ensuring stable manoeuvres regardless of the user's experience. Training our proposed architecture requires much less expert demonstrations compared to standard neural network architectures. Finally, we demonstrate experimentally these results in the in-house quadruped Stoch 2.

In any industrial or software system, predicting future values of measurable parameters well in advance is of utmost importance for avoiding disruptions. The historical data on system parameters measured at regular time intervals can be leveraged to address this long horizon prediction problem. However, complex interdependencies between the parameters and the need for avoiding false recommendations pose challenges in this prediction task. An equally challenging and useful exercise is to identify the 'important' parameters and optimize them in order to attain good system performance. This paper describes a generic framework, along with specific methods, for this data analytics problem and presents a case study on a large-scale enterprise system. The proposed method combines techniques from machine learning, causal analysis, time-series analysis and stochastic optimization to achieve accurate prediction (estimating future values of parameters) and reliable prescription (controlling independent parameters to optimize system performance). The approach is validated with data from a large-scale enterprise service bus consisting of about 30 parameters measured at 5 minute intervals over a period of 6 months.

Humans and animals are believed to use a very minimal set of trajectories to perform a wide variety of tasks including walking. Our main objective in this paper is two fold 1) Obtain an effective tool to realize these basic motion patterns for quadrupedal walking, called the kinematic motion primitives (kMPs), via trajectories learned from deep reinforcement learning (D-RL) and 2) Realize a set of behaviors, namely trot, walk, gallop and bound from these kinematic motion primitives in our custom four legged robot, called the “Stoch”. D-RL is a data driven approach, which has been shown to be very effective for realizing all kinds of robust locomotion behaviors, both in simulation and in experiment. On the other hand, kMPs are known to capture the underlying structure of walking and yield a set of derived behaviors. We first generate walking gaits from D-RL, which uses policy gradient based approaches. We then analyze the resulting walking by using principal component analysis. We observe that the kMPs extracted from PCA followed a similar pattern irrespective of the type of gaits generated. Leveraging on this underlying structure, we then realize walking in Stoch by a straightforward reconstruction of joint trajectories from kMPs. This type of methodology improves the transferability of these gaits to real hardware, lowers the computational overhead on-board, and also avoids multiple training iterations by generating a set of derived behaviors from a single learned gait.

In this work, we provide a simulation framework to perform systematic studies on the effects of spinal joint compliance and actuation on bounding performance of a 16-DOF quadruped spined robot Stoch 2. Fast quadrupedal locomotion with active spine is an extremely hard problem, and involves a complex coordination between the various degrees of freedom. Therefore, past attempts at addressing this problem have not seen much success. Deep-Reinforcement Learning seems to be a promising approach, after its recent success in a variety of robot platforms, and the goal of this paper is to use this approach to realize the aforementioned behaviors. With this learning framework, the robot reached a bounding speed of 2.1m /s with a maximum Froude number of 2. Simulation results also show that use of active spine, indeed, increased the stride length, improved the cost of transport, and also reduced the natural frequency to more realistic values.

In this paper, we explore a specific form of deep reinforcement learning (D-RL) technique for quadrupedal walking—trajectory based policy search via deep policy networks. Existing approaches determine optimal policies for each time step, whereas we propose to determine an optimal policy for each walking step. We justify our approach based on the fact that animals including humans use “low” dimensional trajectories at the joint level to realize walking. We will construct these trajectories by using Bézier polynomials, with the coefficients being determined by a parameterized policy. In order to maintain smoothness of the trajectories during step transitions, hybrid invariance conditions are also applied. The action is computed at the beginning of every step, and a linear PD control law is applied to track at the individual joints. After each step, reward is computed, which is then used to update the new policy parameters for the next step. After learning an optimal policy, i.e., an optimal walking gait for each step, we then successfully play them in a custom built quadruped robot, Stoch 2, thereby validating our approach.

We extend the idea of model-based algorithms for deterministic optimization to simulation optimization over continuous space. Model-based algorithms iteratively generate a population of candidate solutions from a sampling distribution and use the performance of the candidate solutions to update the sampling distribution. By viewing the original simulation optimization problem as another optimization problem over the parameter space of the sampling distribution, we propose to use a direct gradient search on the parameter space to update the sampling distribution. To improve the computational efficiency, we further develop a two-timescale updating scheme that updates the parameter on a slow timescale and estimates the quantities involved in the parameter updating on the fast timescale. We analyze the convergence properties of our algorithms through techniques from stochastic approximation, and demonstrate the good empirical performance by comparing with two state-of-the-art model-based simulation optimization methods. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0771 .

Hadoop MapReduce is a popular framework for distributed storage and processing of large datasets and is used for big data analytics. It has various configuration parameters which play an important role in deciding the performance i.e., the execution time of a given big data processing job. Default values of these parameters do not result in good performance and therefore it is important to tune them. However, there is inherent difficulty in tuning the parameters due to two important reasons - first, the parameter search space is large and second, there are cross-parameter interactions. Hence, there is a need for a dimensionality-free method which can automatically tune the configuration parameters by taking into account the cross-parameter dependencies. In this paper, we propose a novel Hadoop parameter tuning methodology, based on a noisy gradient algorithm known as the simultaneous perturbation stochastic approximation (SPSA). The SPSA algorithm tunes the selected parameters by directly observing the performance of the Hadoop MapReduce system. The approach followed is independent of parameter dimensions and requires only 2 observations per iteration while tuning. We demonstrate the effectiveness of our methodology in achieving good performance on popular Hadoop benchmarks namely Grep, Bigram, Inverted Index, Word Co-occurrence and Terasort. Our method, when tested on a 25 node Hadoop cluster shows 45-66% decrease in execution time of Hadoop jobs on an average, when compared to prior methods. Further, our experiments also indicate that the parameters tuned by our method are resilient to changes in number of cluster nodes, which makes our method suitable to optimize Hadoop when it is provided as a service on the cloud.

In this paper, we provide a new algorithm for the problem of prediction in the model-free MDP setting, i.e., estimating the value function of a given policy using the linear function approximation architecture, with memory and computation costs scaling quadratically in the size of the feature set. The algorithm is a multi-timescale variant of the very popular cross entropy (CE) method which is a model based search method to find the global optimum of a real-valued function. This is the first time a model based search method is used for the prediction problem. A proof of convergence using the ODE method is provided. The theoretical results are supplemented with experimental comparisons. The algorithm achieves good performance fairly consistently on many benchmark problems.

In this paper, we provide for the first time, error bounds for the off-policy prediction in reinforcement learning. The primary objective in off-policy prediction is to estimate the value function of a given target policy of interest using the linear function approximation architecture by utilizing a sample trajectory generated by a behaviour policy which is possibly different from the target policy. The stability of the off-policy prediction has been an open question for a long time. Only recently, could Yu provide a generalized proof, which makes our results more appealing to the reinforcement learning community. The off-policy prediction is useful in complex reinforcement learning settings, where the sample trajectory is hard to obtain and one has to rely on the sample behaviour of the system with respect to an arbitrary policy. We provide here error bound on the solution of the off-policy prediction with respect to a closeness measure between the target and the behaviour policy.

In this paper, we provide a new algorithm for the problem of stochastic global optimization where only noisy versions of the objective function are available. The algorithm is inspired by the well known cross entropy (CE) method. The algorithm takes the shape of a multi-timescale stochastic approximation algorithm, where we reuse the previous samples based on discounted averaging, and hence it saves the overall computational and storage cost. We provide proof of the stability and the global optimization property of our algorithm. The algorithm shows good performance on the noisy versions of global optimization benchmarks and outperforms a state-of-the-art algorithm for non-linear function approximation in reinforcement learning.

In reinforcement learning (RL), an important sub-problem is learning the value function, which is chiefly influenced by the architecture used to represent value functions. is often expressed as a linear combination of a pre-selected set of basis functions. These basis functions are either selected in an ad-hoc manner or are tailored to the RL task using the domain knowledge. Selecting basis functions in an ad-hoc manner does not give a good approximation of value function while choosing functions using domain knowledge introduces dependency on the task. Thus, a desirable scenario is to have a method to choose basis functions that are task independent, but which also provide a good approximation for the value function. In this paper, we propose a novel task-independent basis function construction method that uses the topology of the underlying state space and the reward structure to build the reward-based Proto Value Functions (RPVFs). The approach we propose gives good approximation for the value function and enhanced learning performance. The performance is demonstrated via experiments on grid-world tasks.

The problem of entity resolution is widely studied in the research community, where the goal is to identify real users associated with the user references in the documents. We focus on the problem of entity resolution in dyadic data, where associations between one pair of domain entities such as documents-words and associations between another pair, such as documents-users are observed, the example of which includes bibliographic data. For this problem of entity resolution in bibliographic data, we propose a Bayesian nonparametric `Sparse entity resolution model' (SERM) exploring the sparse relationships between the grouped data i.e., grouping of the documents, and the topics, author entities in the group. Further, we also exploit the sparseness between an author entity and the associated author aliases. Grouping of the documents is achieved with the stick breaking prior for the Dirichlet processes (DP). To achieve sparseness, we propose a solution that introduces separate Indian Buffet process (IBP) priors over topics and the author entities for the groups and k-NN mechanism for selecting author aliases for the author entities. We propose a scalable inference for SERM by appropriately combining partially collapsed Gibbs sampling scheme in Focussed topic model (FTM), inference scheme used for parametric IBP prior and the k-NN mechanism. We perform experiments over bibliographic datasets, Citeseer and Rexa, to show that the proposed SERM model improves the accuracy of entity resolution by finding relevant author entities through modeling sparse relationships and is scalable, when compared to the state-of-the-art baseline.

Markov decision processes (MDPs) with large number of states are of high practical interest. However, conventional algorithms to solve MDP are computationally infeasible in this scenario. Approximate dynamic programming (ADP) methods tackle this issue by computing approximate solutions. A widely applied ADP method is approximate linear program (ALP) which makes use of linear function approximation and offers theoretical performance guarantees. Nevertheless, the ALP is difficult to solve due to the presence of a large number of constraints and in practice, a reduced linear program (RLP) is solved instead. The RLP has a tractable number of constraints sampled from the original constraints of the ALP. Though the RLP is known to perform well in experiments, theoretical guarantees are available only for a specific RLP obtained under idealized assumptions. In this paper, we generalize the RLP to define a generalized reduced linear program (GRLP) which has a tractable number of constraints that are obtained as positive linear combinations of the original constraints of the ALP. The main contribution of this paper is the novel theoretical framework developed to obtain error bounds for any given GRLP. Central to our framework are two max-norm contraction operators. Our result theoretically justifies linear approximation of constraints. We discuss the implication of our results in the contexts of ADP and reinforcement learning. We also demonstrate via an example in the domain of controlled queues that the experiments conform to the theory.

We consider the problem of finding optimal energy sharing policies that maximize the network performance of a system comprising of multiple sensor nodes and a single energy harvesting (EH) source. Sensor nodes periodically sense the random field and generate data, which is stored in the corresponding data queues. The EH source harnesses energy from ambient energy sources and the generated energy is stored in an energy buffer. Sensor nodes receive energy for data transmission from the EH source. The EH source has to efficiently share the stored energy among the nodes to minimize the long-run average delay in data transmission. We formulate the problem of energy sharing between the nodes in the framework of average cost infinite-horizon Markov decision processes (MDPs). We develop efficient energy sharing algorithms, namely Q-learning algorithm with exploration mechanisms based on the ε-greedy method as well as upper confidence bound (UCB) . We extend these algorithms by incorporating state and action space aggregation to tackle state-action space explosion in the MDP. We also develop a cross entropy based method that incorporates policy parameterization to find near optimal energy sharing policies. Through simulations, we show that our algorithms yield energy sharing policies that outperform the heuristic greedy method.

Task starvation leads to huge variation in the completion times of the tasks posted on to the crowd. The price offered to a given task together with the dynamics of the crowd at the time of posting affect its completion time. Large organizations/requesters who frequent the crowd at regular intervals in order to get their tasks done desire predictability in completion times of the tasks. Thus, such requesters have to take into account the crowd dynamics at the time of posting the tasks and price them accordingly. In this work, we study an instance of the pricing problem and propose a solution based on the framework of Markov Decision Processes (MDPs).

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize Gaussian distributions. In this paper, we propose a Smoothed Functional (SF) scheme for gradient estimation using q-Gaussian distribution, and also propose an algorithm for optimization based on the above scheme. Convergence results of the algorithm are presented. Performance of the proposed algorithm is shown by simulation results on a queuing model.

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm.

We consider a stochastic differential equation (SDE) model of slotted Aloha with the retransmission probability as the associated parameter. We formulate the problem in both (a) the finite horizon and (b) the infinite horizon average cost settings. We apply the algorithm of for the first setting, while for the second, we adapt a related algorithm from that was originally developed in the simulation optimization framework. In the first setting, we obtain an optimal parameter trajectory that prescribes the parameter to use at any given instant while in the second setting, we obtain an optimal time-invariant parameter. Our algorithms are seen to exhibit good performance.

We propose, for the first time, a reinforcement learning (RL) algorithm with function approximation for traffic signal control. Our algorithm incorporates state-action features and is easily implementable in high-dimensional settings. Prior work, e.g., the work of Abdulhai, on the application of RL to traffic signal control requires full-state representations and cannot be implemented, even in moderate-sized road networks, because the computational complexity exponentially grows in the numbers of lanes and junctions. We tackle this problem of the curse of dimensionality by effectively using feature-based state representations that use a broad characterization of the level of congestion as low, medium, or high. One advantage of our algorithm is that, unlike prior work based on RL, it does not require precise information on queue lengths and elapsed times at each lane but instead works with the aforementioned described features. The number of features that our algorithm requires is linear to the number of signaled lanes, thereby leading to several orders of magnitude reduction in the computational complexity. We perform implementations of our algorithm on various settings and show performance comparisons with other algorithms in the literature, including the works of Abdulhaiand Cools, as well as the fixed-timing and the longest queue algorithms. For comparison, we also develop an RL algorithm that uses full-state representation and incorporates prioritization of traffic, unlike the work of AbdulhaiWe observe that our algorithm outperforms all the other algorithms on all the road network settings that we consider.

Sutton, Szepesvári and Maei (2009) recently introduced the first temporal-difference learning algorithm compatible with both linear function approximation and off-policy training, and whose complexity scales only linearly in the size of the function approximator. Although their gradient temporal difference (GTD) algorithm converges reliably, it can be very slow compared to conventional linear TD (on on-policy problems where TD is convergent), calling into question its practical utility. In this paper we introduce two new related algorithms with better convergence rates. The first algorithm, GTD2, is derived and proved convergent just as GTD was, but uses a different objective function and converges significantly faster (but still not as fast as conventional TD). The second new algorithm, linear TD with gradient correction, or TDC, uses the same update rule as conventional TD except for an additional term which is initially zero. In our experiments on small test problems and in a Computer Go application with a million features, the learning rate of this algorithm was comparable to that of conventional TD. This algorithm appears to extend linear TD to off-policy learning with no penalty in performance while only doubling computational requirements.

We introduce the first temporal-difference learning algorithms that converge with smooth value function approximators, such as neural networks. Conventional temporal-difference (TD) methods, such as TD($\lambda$), Q-learning and Sarsa have been used successfully with function approximation in many applications. However, it is well known that off-policy sampling, as well as nonlinear function approximation, can cause these algorithms to become unstable (i.e., the parameters of the approximator may diverge). Sutton et al (2009a,b) solved the problem of off-policy learning with linear TD algorithms by introducing a new objective function, related to the Bellman-error, and algorithms that perform stochastic gradient-descent on this function. In this paper, we generalize their work to nonlinear function approximation. We present a Bellman error objective function and two gradient-descent TD algorithms that optimize it. We prove the asymptotic almost-sure convergence of both algorithms for any finite Markov decision process and any smooth value function approximator, under usual stochastic approximation conditions. The computational complexity per iteration scales linearly with the number of parameters of the approximator. The algorithms are incremental and are guaranteed to converge to locally optimal solutions.

We extend Dyna planning architecture for policy evaluation and control in two significant aspects. First, we introduce a multi-step Dyna planning that projects the simulated state/feature many steps into the future. Our multi-step Dyna is based on a multi-step model, which we call the {\em $\lambda$-model}. The $\lambda$-model interpolates between the one-step model and an infinite-step model, and can be learned efficiently online. Second, we use for Dyna control a dynamic multi-step model that is able to predict the results of a sequence of greedy actions and track the optimal policy in the long run. Experimental results show that Dyna using the multi-step model evaluates a policy faster than using single-step models; Dyna control algorithms using the dynamic tracking model are much faster than model-free algorithms; further, multi-step Dyna control algorithms enable the policy and value function to converge much faster to their optima than single-step Dyna algorithms.

With the availability of a huge amount of video data on various sources, efficient video retrieval tools are increasingly in demand. Video being a multi-modal data, the perceptions of ldquorelevancerdquo between the user provided query video (in case of Query-By-Example type of video search) and retrieved video clips are subjective in nature. We present an efficient video retrieval method that takes userpsilas feedback on the relevance of retrieved videos and iteratively reformulates the input query feature vectors (QFV) for improved video retrieval. The QFV reformulation is done by a simple, but powerful feature weight optimization method based on Simultaneous Perturbation Stochastic Approximation (SPSA) technique. A video retrieval system with video indexing, searching and relevance feedback (RF) phases is built for demonstrating the performance of the proposed method. The query and database videos are indexed using the conventional video features like color, texture, etc. However, we use the comprehensive and novel methods of feature representations, and a spatio-temporal distance measure to retrieve the top M videos that are similar to the query. In feedback phase, the user activated iterative on the previously retrieved videos is used to reformulate the QFV weights (measure of importance) that reflect the userpsilas preference, automatically. It is our observation that a few iterations of such feedback are generally sufficient for retrieving the desired video clips. The novel application of SPSA based RF for user-oriented feature weights optimization makes the proposed method to be distinct from the existing ones. The experimental results show that the proposed RF based video retrieval exhibit good performance.

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic rein- forcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their com- patibility with function approximation methods, which are needed to handle large or in(cid:2)nite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further re- duce variance in some cases. Our results extend prior two-timescale convergence results for actor-critic methods by Konda and Tsitsiklis by using temporal differ- ence learning in the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actor-critic methods by Peters, Vijayakumar and Schaal by providing the (cid:2)rst convergence proofs and the (cid:2)rst fully incremental algorithms.

We study the problem of long-run average cost control of Markov chains conditioned on a rare event. In a related recent work, a simulation based algorithm for estimating performance measures associated with a Markov chain conditioned on a rare event has been developed. We extend ideas from this work and develop an adaptive algorithm for obtaining, online, optimal control policies conditioned on a rare event. Our algorithm uses three timescales or step-size schedules. On the slowest timescale, a gradient search algorithm for policy updates that is based on one-simulation simultaneous perturbation stochastic approximation (SPSA) type estimates is used. Deterministic perturbation sequences obtained from appropriate normalized Hadamard matrices are used here. The fast timescale recursions compute the conditional transition probabilities of an associated chain by obtaining solutions to the multiplicative Poisson equation (for a given policy estimate). Further, the risk parameter associated with the value function for a given policy estimate is updated on a timescale that lies in between the two scales above. We briefly sketch the convergence analysis of our algorithm and present a numerical application in the setting of routing multiple flows in communication networks.

A generalized evolutionary algorithm based on Tsallis statistics is proposed. The algorithm uses Tsallis generalized canonical distribution, which is one parameter generalization of Boltzmann distribution, to weigh the configurations in the selection mechanism. This generalization is motivated by the recently proposed generalized simulated annealing algorithm based on Tsallis statistics. We also present an information theoretic justification to use Boltzmann distribution in the selection mechanism, since these 'canonical' distributions have deep roots in information theory. Our simulation results show that for an appropriate choice of non-extensive index that is offered by Tsallis statistics, evolutionary algorithms based on this generalization outperform algorithms based on Boltzmann distribution.

Kullback-Leibler cross-entropy has unique properties in cases involving distributions resulting from cross-entropy minimization. Nonextensive entropy (Tsallis entropy), which is a one-parameter generalization of Shannon entropy, is proposed to study certain class of physical systems. Thermostatistics based on Tsallis entropy is termed as nonextensive statistics or Tsallis statistics. Previously, Kullback-Leibler cross-entropy has been generalized and studied in this framework. In this paper we study properties of generalized cross-entropy minimization and present some differences with the classical case. In the representation of such a minimum cross-entropy distribution, we highlight the use of the q-product, an operator that has been recently introduced, to derive the mathematical structure behind the Tsallis statistics. One of our main results is the generalization of the triangle equality of cross-entropy minimization, in nonextensive framework

Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in practice because a good annealing schedule for the inverse temperature parameter is lacking. In this paper, we propose a Cauchy annealing schedule for Boltzmann selection scheme based on a hypothesis that selection-strength should increase as evolutionary process goes on and distance between two selection strengths should decrease for the process to converge. To formalize these aspects, we develop formalism for selection mechanisms using fitness distributions and give an appropriate measure for selection strength. In this paper, we prove an important result, by which we derive an annealing schedule called Cauchy annealing schedule. We demonstrate the novelty of proposed annealing schedule using simulations in the framework of genetic algorithms.

Darwinian evolution, which is characterized in terms of particular macroscopic behavior that emerges from microscopic organismic interaction, considers populations as units of evolutionary change. We formalize these concepts in evolutionary computation by developing notion of quotient evolutionary space (QES). We map set of all finite populations to a set of macroscopic properties of population those are chosen a priori; and we call this mapping as evolutionary criteria. On the 'quotient set of populations' that is induced by evolutionary criteria, we define mathematical structures to define evolutionary change with respect to chosen macroscopic parameters at populational level. This allows us to transform the objective defined on the search space that is imposed by the fitness function to an objective on the population space. We call quotient set of populations along with the mathematical structures the quotient evolutionary space. To demonstrate the abstraction we consider fitness distribution of population as evolutionary criteria and give a detailed analysis of resulting spaces and basic convergence results.

Optimal structured feedback control policies for rate-based flow control of available bit rate service in asynchronous transfer mode networks are obtained in the presence of information and propagation delays, using a numerically efficient two-timescale simultaneous perturbation stochastic approximation (SPSA) algorithm. Models comprising both a single bottleneck node and a network with multiple bottleneck nodes are considered. A convergence analysis of the algorithm is presented. Numerical experiments demonstrate fast convergence even in the presence of significant delays. We also illustrate performance comparisons with the well-known explicit rate indication for congestion avoidance (ERICA) algorithm and describe another algorithm (based on ERICA) that does not require estimating available bandwidth (as in ERICA).