Imitation learning (IL) is notably effective for robotic tasks where directly programming behaviors or defining optimal control costs is challenging. In this work, we address a scenario where the imitator relies solely on observed behavior and cannot make environmental interactions during learning. It does not have additional supplementary datasets beyond the expert's dataset nor any information about the transition dynamics. Unlike state-of-the-art (SOTA) IL methods, this approach tackles the limitations of conventional IL by operating in a more constrained and realistic setting. Our method uses the Markov balance equation and introduces a novel conditional density estimation-based imitation learning framework. It employs conditional normalizing flows for transition dynamics estimation and aims at satisfying a balance equation for the environment. Through a series of numerical experiments on Classic Control and MuJoCo environments, we demonstrate consistently superior empirical performance compared to many SOTA IL algorithms.

Constrained Markov decision processes (CMDPs) models are increasingly important in many applications with multiple objectives. When the model is unknown and must be learned online, it is desirable to ensure that the constraint is met, or at least the violation is bounded with time. In recent literature, progress has been made on this very challenging problem but with either unsatisfactory assumptions such as the knowledge of a safe policy, or have high cumulative regret. We propose the Safe-PSRL (posterior sampling-based RL) algorithm that does not need such assumptions and yet performs very well, both in terms of theoretical regret bounds as well as empirically. The algorithm efficiently trades-off exploration and exploitation using posterior sampling-based exploration, and yet provably suffers only bounded constraint violation using carefully-crafted pessimism. We establish a sub-linear $\tilde{O}(H^{2.5}\sqrt{|S|^2|A|K})$ upper bound on the Bayesian objective regret along with a bounded, i.e., $\tilde{O}(1)$ constraint-violation regret over $K$ episodes for an $|S|$-state, $|A|$-action, and $H$ horizon CMDP which improves over state-of-the-art algorithms for the same setting.

A major challenge in aligning large language models (LLMs) with human preferences is the issue of distribution shift. LLM alignment algorithms rely on static preference datasets, assuming that they accurately represent real-world user preferences. However, user preferences vary significantly across geographical regions, demographics, linguistic patterns, and evolving cultural trends. This preference distribution shift leads to catastrophic alignment failures in many real-world applications. We address this problem using the principled framework of distributionally robust optimization, and develop two novel distributionally robust direct preference optimization (DPO) algorithms, namely, Wasserstein DPO (WDPO) and Kullback–Leibler DPO (KLDPO). We characterize the sample complexity of learning the optimal policy parameters for WDPO and KLDPO. Moreover, we propose scalable gradient descent-style learning algorithms by developing suitable approximations for the challenging minimax loss functions of WDPO and KLDPO. Our empirical experiments using benchmark data sets and LLMs demonstrate the superior performance of WDPO and KLDPO in substantially improving the alignment when there is a preference distribution shift.

In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $\tilde\mathcal{O}(HS\sqrt{AT})$ in the infinite-horizon zero-sum stochastic games with average-reward criterion. Here $H$ is an upper bound on the span of the bias function, $S$ is the number of states, $A$ is the number of joint actions and $T$ is the horizon. We consider the online setting where the opponent can not be controlled and can take any arbitrary time-adaptive history-dependent strategy. Our regret bound improves on the best existing regret bound of $\tilde\mathcal{O}(\sqrt[3]{DS^2AT^2})$ by Wei et al., (2017) under the same assumption and matches the theoretical lower bound in $T$.

Reinforcement Learning (RL) for constrained MDPs (CMDPs) is an increasingly important problem for various applications. Often, the average criterion is more suitable than the discounted criterion. Yet, RL for average-CMDPs (ACMDPs) remains a challenging problem. Algorithms designed for discounted constrained RL problems often do not perform well for the average CMDP setting. In this paper, we introduce a new policy optimization with function approximation algorithm for constrained MDPs with the average criterion. The Average-Constrained Policy Optimization (ACPO) algorithm is inspired by trust region-based policy optimization algorithms. We develop basic sensitivity theory for average CMDPs, and then use the corresponding bounds in the design of the algorithm. We provide theoretical guarantees on its performance, and through extensive experimental work in various challenging OpenAI Gym environments, show its superior empirical performance when compared to other state-of-the-art algorithms adapted for the ACMDPs.

In this paper, we present the e-COP algorithm, the first policy optimization algorithm for constrained Reinforcement Learning (RL) in episodic (finite horizon) settings. Such formulations are applicable when there are separate sets of optimization criteria and constraints on a system's behavior. We approach this problem by first establishing a policy difference lemma for the episodic setting, which provides the theoretical foundation for the algorithm. Then, we propose to combine a set of established and novel solution ideas to yield the e-COP algorithm that is easy to implement and numerically stable, and provide a theoretical guarantee on optimality under certain scaling assumptions. Through extensive empirical analysis using benchmarks in the Safety Gym suite, we show that our algorithm has similar or better performance than SoTA (non-episodic) algorithms adapted for the episodic setting. The scalability of the algorithm opens the door to its application in safety-constrained Reinforcement Learning from Human Feedback for Large Language or Diffusion Models.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but *the question is how, and by how much?* We show that the degree of improvement must depend on the *quality* of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given *competence* level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

We consider the problem of online reinforcement learning for the Stochastic Shortest Path (SSP) problem modeled as an unknown MDP with an absorbing state. We propose PSRL-SSP, a simple posterior sampling-based reinforcement learning algorithm for the SSP problem. The algorithm operates in epochs. At the beginning of each epoch, a sample is drawn from the posterior distribution on the unknown model dynamics, and the optimal policy with respect to the drawn sample is followed during that epoch. An epoch completes if either the number of visits to the goal state in the current epoch exceeds that of the previous epoch, or the number of visits to any of the state-action pairs is doubled. We establish a Bayesian regret bound of $\tilde{\mathcal{O}}(B_{\ast} S\sqrt{AK})$, where $B_{\ast}$ is an upper bound on the expected cost of the optimal policy, $S$ is the size of the state space, $A$ is the size of the action space, and $K$ is the number of episodes. The algorithm only requires the knowledge of the prior distribution, and has no hyper-parameters to tune. It is the first such posterior sampling algorithm and outperforms numerically previously proposed optimism-based algorithms.

Solving Partially Observable Markov Decision Processes (POMDPs) is hard. Learning optimal controllers for POMDPs when the model is unknown is harder. Online learning of optimal controllers for unknown POMDPs, which requires efficient learning using regret-minimizing algorithms that effectively tradeoff exploration and exploitation, is even harder, and no solution exists currently. In this paper, we consider infinite-horizon average-cost POMDPs with unknown transition model, though a known observation model. We propose a natural posterior sampling-based reinforcement learning algorithm (PSRL-POMDP) and show that it achieves a regret bound of $O(\log T)$, where $T$ is the time horizon, when the parameter set is finite. In the general case (continuous parameter set), we show that the algorithm achieves $O(T^{2/3})$ regret under two technical assumptions. To the best of our knowledge, this is the first online RL algorithm for POMDPs and has sub-linear regret.

We introduce two new no-regret algorithms for the stochastic shortest path (SSP) problem with a linear MDP that significantly improve over the only existing results of (Vial et al., 2021). Our first algorithm is computationally efficient and achieves a regret bound $O(\sqrt{d^3B_{\star}^2T_{\star} K})$, where $d$ is the dimension of the feature space, $B_{\star}$ and $T_{\star}$ are upper bounds of the expected costs and hitting time of the optimal policy respectively, and $K$ is the number of episodes. The same algorithm with a slight modification also achieves logarithmic regret of order $O(\frac{d^3B_{\star}^4}{c_{\min}^2\text{\rm gap}_{\min} }\ln^5\frac{dB_{\star} K}{c_{\min}})$, where $\text{\rm gap}_{\min}$ is the minimum sub-optimality gap and $c_{\min}$ is the minimum cost over all state-action pairs. Our result is obtained by developing a simpler and improved analysis for the finite-horizon approximation of (Cohen et al., 2021) with a smaller approximation error, which might be of independent interest. On the other hand, using variance-aware confidence sets in a global optimization problem, our second algorithm is computationally inefficient but achieves the first “horizon-free” regret bound $O(d^{3.5}B_{\star}\sqrt{K})$ with no polynomial dependency on $T_{\star}$ or $1/c_{\min}$, almost matching the $\Omega(dB_{\star}\sqrt{K})$ lower bound from (Min et al., 2021).

We study regret minimization for infinite-horizon average-reward Markov Decision Processes (MDPs) under cost constraints. We start by designing a policy optimization algorithm with carefully designed action-value estimator and bonus term, and show that for ergodic MDPs, our algorithm ensures $O(\sqrt{T})$ regret and constant constraint violation, where $T$ is the total number of time steps. This strictly improves over the algorithm of (Singh et al., 2020), whose regret and constraint violation are both $O(T^{2/3})$. Next, we consider the most general class of weakly communicating MDPs. Through a finite-horizon approximation, we develop another algorithm with $O(T^{2/3})$ regret and constraint violation, which can be further improved to $O(\sqrt{T})$ via a simple modification, albeit making the algorithm computationally inefficient. As far as we know, these are the first set of provable algorithms for weakly communicating MDPs with cost constraints.

Autonomous agents often operate in environments where the state is partially observed. In addition to maximizing their cumulative reward, agents must execute complex tasks with rich temporal and logical structures. These tasks can be expressed using temporal logic languages like finite linear temporal logic. This paper, for the first time, provides a structured framework for designing agent policies that maximize the reward while ensuring that the probability of satisfying the temporal logic specification is sufficiently high. We reformulate the problem as a constrained partially observable Markov decision process (POMDP) and provide a novel approach that can leverage off-the-shelf unconstrained POMDP solvers for solving it. Our approach guarantees approximate optimality and constraint satisfaction with high probability. We demonstrate its effectiveness by implementing it on several models of interest.

Constrained Markov decision processes (CMDPs) formalize sequential decision-making problems whose objective is to minimize a cost function while satisfying constraints on various cost functions. In this paper, we consider the setting of episodic fixed-horizon CMDPs. We propose an online algorithm which leverages the linear programming formulation of repeated optimistic planning for finite-horizon CMDP to provide a probably approximately correctness (PAC) guarantee on the number of episodes needed to ensure a near optimal policy, i.e., with resulting objective value close to that of the optimal value and satisfying the constraints within low tolerance, with high probability. The number of episodes needed is shown to have linear dependence on the sizes of the state and action spaces and quadratic dependence on the time horizon and an upper bound on the number of possible successor states for a state-action pair. Therefore, if the upper bound on the number of possible successor states is much smaller than the size of the state space, the number of needed episodes becomes linear in the sizes of the state and action spaces and quadratic in the time horizon.

We develop several new algorithms for learning Markov Decision Processes in an infinite-horizon average-reward setting with linear function approximation. Using the optimism principle and assuming that the MDP has a linear structure, we first propose a computationally inefficient algorithm with optimal O(\sqrt{T}) regret and another computationally efficient variant with O(T^{3/4}) regret, where T is the number of interactions. Next, taking inspiration from adversarial linear bandits, we develop yet another efficient algorithm with O(\sqrt{T}) regret under a different set of assumptions, improving the best existing result by Hao et al. (2020) with O(T^{2/3}) regret. Moreover, we draw a connection between this algorithm and the Natural Policy Gradient algorithm proposed by Kakade (2002), and show that our analysis improves the sample complexity bound recently given by Agarwal et al. (2020).

We introduce a generic template for developing regret minimization algorithms in the Stochastic Shortest Path (SSP) model, which achieves minimax optimal regret as long as certain properties are ensured. The key of our analysis is a new technique called implicit finite-horizon approximation, which approximates the SSP model by a finite-horizon counterpart only in the analysis without explicit implementation. Using this template, we develop two new algorithms: the first one is model-free (the first in the literature to our knowledge) and minimax optimal under strictly positive costs; the second one is model-based and minimax optimal even with zero-cost state-action pairs, matching the best existing result from [Tarbouriech et al., 2021b]. Importantly, both algorithms admit highly sparse updates, making them computationally more efficient than all existing algorithms. Moreover, both can be made completely parameter-free.

Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. To our knowledge, this is the first model-free algorithm for general MDPs in this setting. The second algorithm makes use of recent advances in adaptive algorithms for adversarial multi-armed bandits and improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic assumption. This result significantly improves over the $\mathcal{O}(T^{3/4})$ regret achieved by the only existing model-free algorithm by Abbasi-Yadkori et al. (2019) for ergodic MDPs in the infinite-horizon average-reward setting.

We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth rate of episode length. The second stopping criterion happens when the number of visits to any state-action pair is doubled. We establish $\tilde O(HS\sqrt{AT})$ bounds on expected regret under a Bayesian setting, where $S$ and $A$ are the sizes of the state and action spaces, $T$ is time, and $H$ is the bound of the span. This regret bound matches the best available bound for weakly communicating MDPs. Numerical results show it to perform better than existing algorithms for infinite horizon MDPs.

We consider the problem of distributed online learning with multiple players in multiarmed bandit (MAB) models. Each player can pick among multiple arms. When a player picks an arm, it gets a reward. We consider both independent identically distributed (i.i.d.) reward model and Markovian reward model. In the i.i.d. model, each arm is modeled as an i.i.d. process with an unknown distribution with an unknown mean. In the Markovian model, each arm is modeled as a finite, irreducible, aperiodic and reversible Markov chain with an unknown probability transition matrix and stationary distribution. The arms give different rewards to different players. If two players pick the same arm, there is a collision, and neither of them get any reward. There is no dedicated control channel for coordination or communication among the players. Any other communication between the users is costly and will add to the regret. We propose an online index-based distributed learning policy called dUCB4 algorithm that trades off exploration versus exploitation in the right way, and achieves expected regret that grows at most as near- O(log2T). The motivation comes from opportunistic spectrum access by multiple secondary users in cognitive radio networks wherein they must pick among various wireless channels that look different to different users. This is the first distributed learning algorithm for multiplayer MABs with heterogeneous players (that have player-dependent rewards) to the best of our knowledge.

Development of dynamic spectrum access and allocation techniques recently have made feasible the vision of cognitive radio systems. However, a fundamental question arises: Why would licensed primary users of a spectrum band allow secondary users to share the band and degrade performance for them? And how can we design incentive schemes to enable spectrum sharing using cooperative communication schemes? We consider a principal-agent framework, and propose a contracts-based approach. First, a single primary and a single secondary transmitter-receiver pair with a Gaussian interference channel between them are considered. The two users may contract to cooperate in doing successive-interference cancellation. Under full information, we give equilibrium contracts for various channel conditions. These equilibrium contracts yield Pareto-optimal rate allocations when physically possible. We then allow for time-sharing and observe that in equilibrium contracts there is no actual time-sharing. We show that the designed contracts can be made robust to deviation by either user post-contract. We also show how these can be extended to multiple secondary users. We show that under hidden information, when the primary user has a dominant role, neither user has an incentive to lie about their direct channel coefficients, or manipulate the cross channel measurements, and Pareto-optimal outcomes are achieved at equilibrium.

Various cooperative communication schemes have been proposed as a means to increase the capacity of wireless networks. All such schemes assume that users in the network will cooperate perfectly. However, in a decentralized network this assumption is far from true. Users are selfish and care only about their own rates. They can strategically deviate from their agreed role in such cooperative communication schemes leading to a possible degradation for all. In this paper, we study the incentives for cooperative relaying in a simple model, namely the generalized Gaussian relay channel model (or MAC-GF). We characterize all the Nash equilibrium rates and compare it with the Pareto-optimal rates of the generalized Gaussian relay channel model. granted.

The strategic behavior of receivers (players) in a multiple-input multiple-output Gaussian broadcast channel is investigated using the framework of non-cooperative game theory. In contrast to the non-cooperative Gaussian multiple access channel game in which each player's feasible set of actions is independent of the actions of other players, the action space of receivers in the Gaussian broadcast channel is mutually coupled, usually by a sum power or joint covariance constraint, and hence cannot be treated using traditional Nash equilibrium solution concepts. To characterize the strategic behavior of receivers in a broadcast channel game, this paper treats the broadcast channel power allocation (or covariance matrix selection) as a generalized Nash equilibrium problem with common constraints. The concept of normalized equilibrium (NoE) is used to characterize the equilibria and the existence and uniqueness of NoEs are proven for key scenarios.

Motivated by allocation of bandwidth, wireless spectrum and cloud computing services in secondary network markets, we introduce a hierarchical auction model for network resource allocation. A Tier 1 provider owns a homogeneous network resource and holds an auction to allocate this resource among Tier 2 operators, who in turn allocate the acquired resource among Tier 3 entities. The Tier 2 operators play the role of middlemen, since their utilities for the resource depend on the revenues gained from resale. We first consider static hierarchical auction mechanisms for indivisible resources. We study a class of mechanisms wherein each sub-mechanism is either a first-price or VCG auction, and show that incentive compatibility and efficiency cannot be simultaneously achieved. We also briefly discuss sequential auctions as well as the incomplete information setting. We then propose two VCG-type hierarchical mechanisms for divisible resources. The first one is composed of single-sided auctions at each tier, while the second one employs double-sided auctions at all tiers except Tier 1. Both mechanisms induce an efficient Nash equilibrium.

We formulate the following combinatorial multi-armed bandit (MAB) problem: There areNrandom variables with unknown mean that are each instantiated in an i.i.d. fashion over time. At each time multiple random variables can be selected, subject to an arbitrary constraint on weights associated with the selected variables. All of the selected individual random variables are observed at that time, and a linearly weighted combination of these selected variables is yielded as the reward. The goal is to find a policy that minimizes regret, defined as the difference between the reward obtained by a genie that knows the mean of each random variable, and that obtained by the given policy. This formulation is broadly applicable and useful for stochastic online versions of many interesting tasks in networks that can be formulated as tractable combinatorial optimization problems with linear objective functions, such as maximum weighted matching, shortest path, and minimum spanning tree computations. Prior work on multi-armed bandits with multiple plays cannot be applied to this formulation because of the general nature of the constraint. On the other hand, the mapping of all feasible combinations to arms allows for the use of prior work on MAB with single-play, but results in regret, storage, and computation growing exponentially in the number of unknown variables. We present new efficient policies for this problem that are shown to achieve regret that grows logarithmically with time, and polynomially in the number of unknown variables. Furthermore, these policies only require storage that grows linearly in the number of unknown parameters. For problems where the underlying deterministic problem is tractable, these policies further require only polynomial computation. For computationally intractable problems, we also present results on a different notion of regret that is suitable when a polynomial-time approximation algorithm is used.

Cooperation between rational users has emerged as a new networking paradigm to improve the performance of wireless networks. In this paper, transmitter cooperation between wireless nodes in a Gaussian multiple access channel is studied under the framework of coalitional game theory. The stability of the grand coalition, the coalition of all users, is studied by modeling the game in partition form, in contrast to previous approaches using characteristic form games, in scenarios with infinite and finite cooperation capacity between transmitters. In both cases, irrespective of the channel gains, the grand coalition is shown to be the sum rate optimal and stable, in the sense that users do not have any incentive to leave the coalition.

We extend the probably approximately correct (PAC) model of learning to Markov decision processes (MDPs) and dynamic games. We obtain simulation-based uniform sample complexity bounds for value function estimates of discounted reward MDPs. We also obtain uniform sample complexity results for Markov games with a finite number of players.

Supporting quality of service (QoS) guarantees in wireless networks requires that admission control algorithms incorporate user mobility, and limit the probability that sufficient resources are unavailable when a user must handoff. We develop a framework for designing admission control algorithms in wireless networks that support guaranteed QoS. First, we devise a taxonomy to explore the mathematical structure and practical design tradeoffs encountered in developing admission control algorithms. We next introduce the perfect knowledge admission control algorithm, which, while unrealizable in practice, serves as a benchmark for evaluating admission control algorithms by using future knowledge of handoff events to exactly control the admissible region. Finally, we perform an extensive set of simulations (including trace-driven simulations) and, applying the perfect knowledge algorithm, we study several admission control algorithm from the literature, identify a number of key system parameters for algorithm design, and quantify the fundamental tradeoffs in complexity and accuracy as revealed by the taxonomy.