Representation learning is increasingly applied to generate representations that generalize well across multiple downstream tasks. Ensuring fairness guarantees in representation learning is crucial to prevent unfairness toward specific demographic groups in downstream tasks. In this work, we formally introduce the task of learning representations that achieve high-confidence fairness. We aim to guarantee that demographic disparity in every downstream prediction remains bounded by a *user-defined* error threshold $\epsilon$, with *controllable* high probability. To this end, we propose the ***F**air **R**epresentation learning with high-confidence **G**uarantees (FRG)* framework, which provides these high-confidence fairness guarantees by leveraging an optimized adversarial model. We empirically evaluate FRG on three real-world datasets, comparing its performance to six state-of-the-art fair representation learning methods. Our results demonstrate that FRG consistently bounds unfairness across a range of downstream models and tasks.

Recent works have studied fair resource allocation in social settings, where fairness is judged by the impact of allocation decisions rather than more traditional minimum or maximum thresholds on the allocations themselves. Our work significantly adds to this literature by developing continuous resource allocation strategies that adhere to *equality of impact*, a generalization of equality of opportunity. We derive methods to maximize total welfare across groups subject to minimal violation of equality of impact, in settings where the outcomes of allocations are unknown but have a diminishing marginal effect. While focused on a two-group setting, our study addresses a broader class of welfare dynamics than explored in prior work. Our contributions are threefold. First, we introduce *Equality of Impact (EoI)*, a fairness criterion defined via group-level impact functions. Second, we design an online algorithm for non-noisy settings that leverages the problem’s geometric structure and achieves constant cumulative fairness regret. Third, we extend this approach to noisy environments with a meta-algorithm and empirically demonstrate that our methods find fair allocations and perform competitively relative to representative baselines.

Machine learning models are often designed to maximize a primary goal, such as accuracy. However, as these models are increasingly used to inform decisions that affect people's lives or well-being, it is often unclear what the real-world repercussions of their deployment might be—making it crucial to understand and manage such repercussions effectively. Models maximizing user engagement on social media platforms, e.g., may inadvertently contribute to the spread of misinformation and content that deepens political polarization. This issue is not limited to social media—it extends to other applications where machine learning-informed decisions can have real-world repercussions, such as education, employment, and lending. Existing methods addressing this issue require prior knowledge or estimates of analytical models describing the relationship between a classifier's predictions and their corresponding repercussions. We introduce Theia, a novel classification algorithm capable of optimizing a primary objective, such as accuracy, while providing high-confidence guarantees about its potential repercussions. Importantly, Theia solves the open problem of providing such guarantees based solely on existing data with observations of previous repercussions. We prove that it satisfies constraints on a model's repercussions with high confidence and that it is guaranteed to identify a solution, if one exists, given sufficient data. We empirically demonstrate, using real-life data, that Theia can identify models that achieve high accuracy while ensuring, with high confidence, that constraints on their repercussions are satisfied.

In this paper, we introduce a fresh perspective on the challenges of credit assignment and policy evaluation. First, we delve into the nuances of eligibility traces and explore instances where their updates may result in unexpected credit assignment to preceding states. From this investigation emerges the concept of a novel value function, which we refer to as the ????????????? ????? ????????. Unlike traditional state value functions, bidirectional value functions account for both future expected returns (rewards anticipated from the current state onward) and past expected returns (cumulative rewards from the episode's start to the present). We derive principled update equations to learn this value function and, through experimentation, demonstrate its efficacy in enhancing the process of policy evaluation. In particular, our results indicate that the proposed learning approach can, in certain challenging contexts, perform policy evaluation more rapidly than TD(λ)–a method that learns forward value functions, v^π, ????????. Overall, our findings present a new perspective on eligibility traces and potential advantages associated with the novel value function it inspires, especially for policy evaluation.

Novel reinforcement learning algorithms, or improvements on existing ones, are commonly justified by evaluating their performance on benchmark environments and are compared to an ever-changing set of standard algorithms. However, despite numerous calls for improvements, experimental practices continue to produce misleading or unsupported claims. One reason for the ongoing substandard practices is that conducting rigorous benchmarking experiments requires substantial computational time. This work investigates the sources of increased computation costs in rigorous experiment designs. We show that conducting rigorous performance benchmarks will likely have computational costs that are often prohibitive. As a result, we argue for using an additional experimentation paradigm to overcome the limitations of benchmarking.

Evaluating policies using off-policy data is crucial for applying reinforcement learning to real-world problems such as healthcare and autonomous driving. Previous methods for *off-policy evaluation* (OPE) generally suffer from high variance or irreducible bias, leading to unacceptably high prediction errors. In this work, we introduce STAR, a framework for OPE that encompasses a broad range of estimators -- which include existing OPE methods as special cases -- that achieve lower mean squared prediction errors. STAR leverages state abstraction to distill complex, potentially continuous problems into compact, discrete models which we call *abstract reward processes* (ARPs). Predictions from ARPs estimated from off-policy data are provably consistent (asymptotically correct). Rather than proposing a specific estimator, we present a new framework for OPE and empirically demonstrate that estimators within STAR outperform existing methods. The best STAR estimator outperforms baselines in all twelve cases studied, and even the median STAR estimator surpasses the baselines in seven out of the twelve cases.

We consider the task of evaluating a policy for a Markov decision process (MDP). The standard unbiased technique for evaluating a policy is to deploy the policy and observe its performance. We show that the data collected from deploying a different policy, commonly called the behavior policy, can be used to produce unbiased estimates with lower mean squared error than this standard technique. We derive an analytic expression for a minimal variance behavior policy -- a behavior policy that minimizes the mean squared error of the resulting estimates. Because this expression depends on terms that are unknown in practice, we propose a novel policy evaluation sub-problem, behavior policy search: searching for a behavior policy that reduces mean squared error. We present two behavior policy search algorithms and empirically demonstrate their effectiveness in lowering the mean squared error of policy performance estimates.

In this work, we consider the off-policy policy evaluation problem for contextual bandits and finite horizon reinforcement learning in the nonstationary setting. Reusing old data is critical for policy evaluation, but existing estimators that reuse old data introduce large bias such that we can not obtain a valid confidence interval. Inspired from a related field called survey sampling, we introduce a variant of the doubly robust (DR) estimator, called the regression-assisted DR estimator, that can incorporate the past data without introducing a large bias. The estimator unifies several existing off-policy policy evaluation methods and improves on them with the use of auxiliary information and a regression approach. We prove that the new estimator is asymptotically unbiased, and provide a consistent variance estimator to a construct a large sample confidence interval. Finally, we empirically show that the new estimator improves estimation for the current and future policy values, and provides a tight and valid interval estimation in several nonstationary recommendation environments.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn \emph{behavior alignment reward functions}. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality---some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

There are reinforcement learning scenarios - e.g., in medicine - where we are compelled to be as confident as possible that a policy change will result in an improvement before implementing it. In such scenarios, we can employ off-policy evaluation (OPE). The basic idea of OPE is to record histories of behaviors under the current policy, and then develop an estimate of the quality of a proposed new policy, seeing what the behavior would have been under the new policy. As we are evaluating the policy without actually using it, we have the "off-policy" of OPE. Applying a concentration inequality to the estimate, we derive a confidence interval for the expected quality of the new policy. If the confidence interval lies above that of the current policy, we can change policies with high confidence that we will do no harm. We focus here on the mathematics of this method, by mechanizing the soundness of off-policy evaluation. A natural side effect of the mechanization is both to clarify all the result’s mathematical assumptions and preconditions, and to further develop HOL4’s library of verified statistical mathematics, including concentration inequalities. Of more significance, the OPE method relies on importance sampling, whose soundness we prove using a measure-theoretic approach. In fact, we generalize the standard result, showing it for contexts comprising both discrete and continuous probability distributions.

Methods for sequential decision-making are often built upon a foundational assumption that the underlying decision process is stationary. This limits the application of such methods because real-world problems are often subject to changes due to external factors (\textit{passive} non-stationarity), changes induced by interactions with the system itself (\textit{active} non-stationarity), or both (\textit{hybrid} non-stationarity). In this work, we take the first steps towards the fundamental challenge of on-policy and off-policy evaluation amidst structured changes due to active, passive, or hybrid non-stationarity. Towards this goal, we make a \textit{higher-order stationarity} assumption such that non-stationarity results in changes over time, but the way changes happen is fixed. We propose, OPEN, an algorithm that uses a double application of counterfactual reasoning and a novel importance-weighted instrument-variable regression to obtain both a lower bias and a lower variance estimate of the structure in the changes of a policy's past performances. Finally, we show promising results on how OPEN can be used to predict future performances for several domains inspired by real-world applications that exhibit non-stationarity.

We present several classes of reinforcement learning algorithms that safely generalize to Markov decision processes (MDPs) not seen during training. Specifically, we study the setting in which some set of MDPs is accessible for training. The goal is to generalize safely to MDPs that are sampled from the same distribution, but which may not be in the set accessible for training. For various definitions of safety, our algorithms give probabilistic guarantees that agents can safely generalize to MDPs that are sampled from the same distribution but are not necessarily in the training set. These algorithms are a type of Seldonian algorithm (Thomas et al., 2019), which is a class of machine learning algorithms that return models with probabilistic safety guarantees for user-specified definitions of safety.

Hindsight allows reinforcement learning agents to leverage new observations to make inferences about earlier states and transitions. In this paper, we exploit the idea of hindsight and introduce posterior value functions. Posterior value functions are computed by inferring the posterior distribution over hidden components of the state in previous timesteps and can be used to construct novel unbiased baselines for policy gradient methods. Importantly, we prove that these baselines reduce (and never increase) the variance of policy gradient estimators compared to traditional state value functions. While the posterior value function is motivated by partial observability, we extend these results to arbitrary stochastic MDPs by showing that hindsight-capable agents can model stochasticity in the environment as a special case of partial observability. Finally, we introduce a pair of methods for learning posterior value functions and prove their convergence.

Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding’s inequality that use weaker assumptions but produce much looser (wider) intervals. In 1969, \citet{Anderson1969} proposed a mean confidence interval strictly better than or equal to Hoeffding’s whose only assumption is that the distribution’s support is contained in an interval $[a,b]$. For the first time since then, we present a new family of bounds that compares favorably to Anderson’s. We prove that each bound in the family has {\em guaranteed coverage}, i.e., it holds with probability at least $1-\alpha$ for all distributions on an interval $[a,b]$. Furthermore, one of the bounds is tighter than or equal to Anderson’s for all samples. In simulations, we show that for many distributions, the gain over Anderson’s bound is substantial.

When faced with sequential decision-making problems, it is often useful to be able to predict what would happen if decisions were made using a new policy. Those predictions must often be based on data collected under some previously used decision-making rule. Many previous methods enable such off-policy (or counterfactual) estimation of the expected value of a performance measure called the return. In this paper, we take the first steps towards a 'universal off-policy estimator' (UnO)---one that provides off-policy estimates and high-confidence bounds for any parameter of the return distribution. We use UnO for estimating and simultaneously bounding the mean, variance, quantiles/median, inter-quantile range, CVaR, and the entire cumulative distribution of returns. Finally, we also discuss UnO's applicability in various settings, including fully observable, partially observable (i.e., with unobserved confounders), Markovian, non-Markovian, stationary, smoothly non-stationary, and discrete distribution shifts.

Structural credit assignment in neural networks is a long-standing problem, with a variety of alternatives to backpropagation proposed to allow for local training of nodes. One of the early strategies was to treat each node as an agent and use a reinforcement learning method called REINFORCE to update each node locally with only a global reward signal. In this work, we revisit this approach and investigate if we can leverage other reinforcement learning approaches to improve learning. We first formalize training a neural network as a finite-horizon reinforcement learning problem and discuss how this facilitates using ideas from reinforcement learning like off-policy learning. We show that the standard on-policy REINFORCE approach, even with a variety of variance reduction approaches, learns suboptimal solutions. We introduce an off-policy approach, to facilitate reasoning about the greedy action for other agents and help overcome stochasticity in other agents. We conclude by showing that these networks of agents can be more robust to correlated samples when learning online.

We study the problem of Safe Policy Improvement (SPI) under constraints in the offline Reinforcement Learning (RL) setting. We consider the scenario where: (i) we have a dataset collected under a known baseline policy, (ii) multiple reward signals are received from the environment inducing as many objectives to optimize. We present an SPI formulation for this RL setting that takes into account the preferences of the algorithm’s user for handling the trade-offs for different reward signals while ensuring that the new policy performs at least as well as the baseline policy along each individual objective. We build on traditional SPI algorithms and propose a novel method based on Safe Policy Iteration with Baseline Bootstrapping (SPIBB, Laroche et al., 2019) that provides high probability guarantees on the performance of the agent in the true environment. We show the effectiveness of our method on a synthetic grid-world safety task as well as in a real-world critical care context to learn a policy for the administration of IV fluids and vasopressors to treat sepsis.

Many sequential decision making problems are high-stakes and require off-policy evaluation (OPE) of a new policy using historical data collected using some other policy. One of the most common OPE techniques that provides unbiased estimates is trajectory based importance sampling (IS). However, due to the high variance of trajectory IS estimates, importance sampling methods based on state-action visitation distributions (SIS) have recently been adopted. Unfortunately, while SIS often provides lower variance estimates for long horizons, estimating the state-action distribution ratios can be challenging and lead to biased estimates. In this paper, we present a new perspective on this bias-variance trade-off and show the existence of a spectrum of estimators whose endpoints are SIS and IS. Additionally, we also establish a spectrum for doubly-robust and weighted version of these estimators. We provide empirical evidence that estimators in this spectrum can be used to trade-off between the bias and variance of IS and SIS and can achieve lower mean-squared error than both IS and SIS.

We propose AC-CRS, a novel conversational recommendation system based on reinforcement learning that better models user interaction compared to prior work. Interactive recommender systems expect an initial request from a user and then iterate by asking questions or recommending potential matching items, continuing until some stopping criterion is achieved. Unlike most existing works that stop as soon as an item is recommended, we model the more realistic expectation that the interaction will continue if the item is not appropriate. Using this process, AC-CRS is able to support a more flexible conversation with users. Unlike existing models, AC-CRS is able to estimate a value for each question in the conversation to make sure that questions asked by the agent are relevant to the target item (i.e., user needs). We also model the possibility that the system could suggest more than one item in a given turn, allowing it to take advantage of screen space if it is present. AC-CRS also better accommodates the massive space of items that a real-world recommender system must handle. Experiments on real-world user purchasing data show the effectiveness of our model in terms of standard evaluation measures such as NDCG.

The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not efficiently capture the setting where the set of available decisions (actions) at each time step is stochastic. Recently, the stochastic action set Markov decision process (SAS-MDP) formulation has been proposed, which better captures the concept of a stochastic action set. In this paper we argue that existing RL algorithms for SAS-MDPs can suffer from potential divergence issues, and present new policy gradient algorithms for SAS-MDPs that incorporate variance reduction techniques unique to this setting, and provide conditions for their convergence. We conclude with experiments that demonstrate the practicality of our approaches on tasks inspired by real-life use cases wherein the action set is stochastic.

In many real-world sequential decision making problems, the number of available actions (decisions) can vary over time. While problems like catastrophic forgetting, changing transition dynamics, changing rewards functions, etc. have been well-studied in the lifelong learning literature, the setting where the size of the action set changes remains unaddressed. In this paper, we present first steps towards developing an algorithm that autonomously adapts to an action set whose size changes over time. To tackle this open problem, we break it into two problems that can be solved iteratively: inferring the underlying, unknown, structure in the space of actions and optimizing a policy that leverages this structure. We demonstrate the efficiency of this approach on large-scale real-world lifelong learning problems.

Most reinforcement learning methods are based upon the key assumption that the transition dynamics and reward functions are fixed, that is, the underlying Markov decision process is stationary. However, in many real-world applications, this assumption is violated, and using existing algorithms may result in a performance lag. To proactively search for a good future policy, we present a policy gradient algorithm that maximizes a forecast of future performance. This forecast is obtained by fitting a curve to the counter-factual estimates of policy performance over time, without explicitly modeling the underlying non-stationarity. The resulting algorithm amounts to a non-uniform reweighting of past data, and we observe that minimizing performance over some of the data from past episodes can be beneficial when searching for a policy that maximizes future performance. We show that our algorithm, called Prognosticator, is more robust to non-stationarity than two online adaptation techniques, on three simulated problems motivated by real-world applications.

Performance evaluations are critical for quantifying algorithmic advances in reinforcement learning. Recent reproducibility analyses have shown that reported performance results are often inconsistent and difficult to replicate. In this work, we argue that the inconsistency of performance stems from the use of flawed evaluation metrics. Taking a step towards ensuring that reported results are consistent, we propose a new comprehensive evaluation methodology for reinforcement learning algorithms that produces reliable measurements of performance both on a single environment and when aggregated across environments. We demonstrate this method by evaluating a broad class of reinforcement learning algorithms on standard benchmark tasks.

Coagent policy gradient algorithms (CPGAs) are reinforcement learning algorithms for training a class of stochastic neural networks called coagent networks. In this work, we prove that CPGAs converge to locally optimal policies. Additionally, we extend prior theory to encompass asynchronous and recurrent coagent networks. These extensions facilitate the straightforward design and analysis of hierarchical reinforcement learning algorithms like the option-critic, and eliminate the need for complex derivations of customized learning rules for these algorithms.

Many real-world sequential decision-making problems involve critical systems with financial risks and human-life risks. While several works in the past have proposed methods that are safe for deployment, they assume that the underlying problem is stationary. However, many real-world problems of interest exhibit non-stationarity, and when stakes are high, the cost associated with a false stationarity assumption may be unacceptable. We take the first steps towards ensuring safety, with high confidence, for smoothly-varying non-stationary decision problems. Our proposed method extends a type of safe algorithm, called a Seldonian algorithm, through a synthesis of model-free reinforcement learning with time-series analysis. Safety is ensured using sequential hypothesis testing of a policy’s forecasted performance, and confidence intervals are obtained using wild bootstrap.

We analyze the extent to which existing methods rely on accurate training data for a specific class of reinforcement learning (RL) algorithms, known as Safe and Seldonian RL. We introduce a new measure of security to quantify the susceptibility to perturbations in training data by creating an attacker model that represents a worst-case analysis, and show that a couple of Seldonian RL methods are extremely sensitive to even a few data corruptions. We then introduce a new algorithm that is more robust against data corruptions, and demonstrate its usage in practice on some RL problems, including a grid-world and a diabetes treatment simulation.

The recently proposed option-critic architecture (Bacon, Harb, and Precup 2017) provides a stochastic policy gradient approach to hierarchical reinforcement learning. Specifically, it provides a way to estimate the gradient of the expected discounted return with respect to parameters that define a finite number of temporally extended actions, called options. In this paper we show how the option-critic architecture can be extended to estimate the natural gradient (Amari 1998) of the expected discounted return. To this end, the central questions that we consider in this paper are: 1) what is the definition of the natural gradient in this context, 2) what is the Fisher information matrix associated with an option’s parameterized policy, 3) what is the Fisher information matrix associated with an option’s parameterized termination function, and 4) how can a compatible function approximation approach be leveraged to obtain natural gradient estimates for both the parameterized policy and parameterized termination functions of an option with per-time-step time and space complexity linear in the total number of parameters. Based on answers to these questions we introduce the natural option critic algorithm. Experimental results showcase improvement over the vanilla gradient approach.

Most model-free reinforcement learning methods leverage state representations (embeddings) for generalization, but either ignore structure in the space of actions or assume the structure is provided a priori. We show how a policy can be decomposed into a component that acts in a low-dimensional space of action representations and a component that transforms these representations into actual actions. These representations improve generalization over large, finite action sets by allowing the agent to infer the outcomes of actions similar to actions already taken. We provide an algorithm to both learn and use action representations and provide conditions for its convergence. The efficacy of the proposed method is demonstrated on large-scale real-world problems.

In this paper we derive new concentration inequalities for the conditional value at risk (CVaR) of a random variable, and compare them to the previous state of the art (Brown, 2007). We show analytically that our lower bound is strictly tighter than Brown’s, and empirically that this difference is significant. While our upper bound may be looser than Brown’s in some cases, we show empirically that in most cases our bound is significantly tighter. After discussing when each upper bound is superior, we conclude with empirical results which suggest that both of our bounds will often be significantly tighter than Brown’s.

In this paper we consider the problem of how a reinforcement learning agent that is tasked with solving a sequence of reinforcement learning problems (a sequence of Markov decision processes) can use knowledge acquired early in its lifetime to improve its ability to solve new problems. We argue that previous experience with similar problems can provide an agent with information about how it should explore when facing a new but related problem. We show that the search for an optimal exploration strategy can be formulated as a reinforcement learning problem itself and demonstrate that such strategy can leverage patterns found in the structure of related problems. We conclude with experiments that show the benefits of optimizing an exploration strategy using our proposed framework.

We present RobinHood, an offline contextual bandit algorithm designed to satisfy a broad family of fairness constraints. Our algorithm accepts multiple fairness definitions and allows users to construct their own unique fairness definitions for the problem at hand. We provide a theoretical analysis of RobinHood, which includes a proof that it will not return an unfair solution with probability greater than a user-specified threshold. We validate our algorithm on three applications: a tutoring system in which we conduct a user study and consider multiple unique fairness definitions; a loan approval setting (using the Statlog German credit data set) in which well-known fairness definitions are applied; and criminal recidivism (using data released by ProPublica). In each setting, our algorithm is able to produce fair policies that achieve performance competitive with other offline and online contextual bandit algorithms.

In machine learning, learning often corresponds to changing the parameters of a parameterized function. A learning rule is an algorithm or mathematical expression that specifies precisely how the parameters should be changed. When creating a machine learning system, we must make two decisions: what representation should be used (i.e., what parameterized function should be used) and what learning rule should be used to search through the resulting set of representable functions. In this paper we focus on gradient-like learning rules, wherein these two decisions are coupled in a subtle (and often unintentional) way. Using most learning rules, these two decisions are coupled in a subtle (and often unintentional) way. That is, using the same learning rule with two different representations that can represent the same sets of functions can result in two different outcomes. After arguing that this coupling is undesirable, particularly when using neural networks, we present a method for partially decoupling these two decisions for a broad class of gradient-like learning rules that span unsupervised learning, reinforcement learning, and supervised learning.

We consider the problem of off-policy policy selection in reinforcement learning: using historical data generated from running one policy to compare two or more policies. We show that approaches based on importance sampling can be unfair---they can select the worse of two policies more often than not. We then give an example that shows importance sampling is systematically unfair in a practically relevant setting; namely, we show that it unreasonably favors shorter trajectory lengths. We then present sufficient conditions to theoretically guarantee fairness. Finally, we provide a practical importance sampling-based estimator to help mitigate the unfairness due to varying trajectory lengths.

Importance sampling is often used in machine learning when training and testing data come from different distributions. In this paper we propose a new variant of importance sampling that can reduce the variance of importance samplingbased estimates by orders of magnitude when the supports of the training and testing distributions differ. After motivating and presenting our new importance sampling estimator, we provide a detailed theoretical analysis that characterizes both its bias and variance relative to the ordinary importance sampling estimator (in various settings, which include cases where ordinary importance sampling is biased, while our new estimator is not, and vice versa). We conclude with an example of how our new importance sampling estimator can be used to improve estimates of how well a new treatment policy for diabetes will work for an individual, using only data from when the individual used a previous treatment policy.

We consider the task of evaluating a policy for a Markov decision process (MDP). The standard unbiased technique for evaluating a policy is to deploy the policy and observe its performance. We show that the data collected from deploying a different policy, commonly called the behavior policy, can be used to produce unbiased estimates with lower mean squared error than this standard technique. We derive an analytic expression for the optimal behavior policy — the behavior policy that minimizes the mean squared error of the resulting estimates. Because this expression depends on terms that are unknown in practice, we propose a novel policy evaluation sub-problem, behavior policy search: searching for a behavior policy that reduces mean squared error. We present a behavior policy search algorithm and empirically demonstrate its effectiveness in lowering the mean squared error of policy performance estimates.

Evaluating a policy by deploying it in the real world can be risky and costly. Off-policy policy evaluation (OPE) algorithms use historical data collected from running a previous policy to evaluate a new policy, which provides a means for evaluating a policy without requiring it to ever be deployed. Importance sampling is a popular OPE method because it is robust to partial observability and works with continuous states and actions. However, the amount of historical data required by importance sampling can scale exponentially with the horizon of the problem: the number of sequential decisions that are made. We propose using policies over temporally extended actions, called options, and show that combining these policies with importance sampling can significantly improve performance for long-horizon problems. In addition, we can take advantage of special cases that arise due to options-based policies to further improve the performance of importance sampling. We further generalize these special cases to a general covariance testing rule that can be used to decide which weights to drop in an IS estimate, and derive a new IS algorithm called Incremental Importance Sampling that can provide significantly more accurate estimates for a broad class of domains.

This paper introduces new optimality-preserving operators on Q-functions. We first describe an operator for tabular representations, the consistent Bellman operator, which incorporates a notion of local policy consistency. We show that this local consistency leads to an increase in the action gap at each state; increasing this gap, we argue, mitigates the undesirable effects of approximation and estimation errors on the induced greedy policies. This operator can also be applied to discretized continuous space and time problems, and we provide empirical results evidencing superior performance in this context. Extending the idea of a locally consistent operator, we then derive sufficient conditions for an operator to preserve optimality, leading to a family of operators which includes our consistent Bellman operator. As corollaries we provide a proof of optimality for Baird's advantage learning algorithm and derive other gap-increasing operators with interesting properties. We conclude with an empirical study on 60 Atari 2600 games illustrating the strong potential of these new operators.

In this paper we present a new way of predicting the performance of a reinforcement learning policy given historical data that may have been generated by a different policy. The ability to evaluate a policy from historical data is important for applications where the deployment of a bad policy can be dangerous or costly. We show empirically that our algorithm produces estimates that often have orders of magnitude lower mean squared error than existing methods—it makes more efficient use of the available data. Our new estimator is based on two advances: an extension of the doubly robust estimator (Jiang & Li, 2015), and a new way to mix between model based and importance sampling based estimates.

We propose a new class of algorithms for minimizing or maximizing functions of parametric probabilistic models. These new algorithms are natural gradient algorithms that leverage more information than prior methods by using a new metric tensor in place of the commonly used Fisher information matrix. This new metric tensor is derived by computing directions of steepest ascent where the distance between distributions is measured using an approximation of energy distance (as opposed to Kullback-Leibler divergence, which produces the Fisher information matrix), and so we refer to our new ascent direction as the energetic natural gradient.

High-level spinal cord injury (SCI) in humans causes paralysis below the neck. Functional electrical stimulation (FES) technology applies electrical current to nerves and muscles to restore movement, and controllers for upper extremity FES neuroprostheses calculate stimulation patterns to produce desired arm movement. However, currently available FES controllers have yet to restore natural movements. Reinforcement learning (RL) is a reward-driven control technique; it can employ user-generated rewards, and human preferences can be used in training. To test this concept with FES, we conducted simulation experiments using computer-generated “pseudo-human” rewards. Rewards with varying properties were used with an actor-critic RL controller for a planar two-degree-of-freedom biomechanical human arm model performing reaching movements. Results demonstrate that sparse, delayed pseudo-human rewards permit stable and effective RL controller learning. The frequency of reward is proportional to learning success, and human-scale sparse rewards permit greater learning than exclusively automated rewards. Diversity of training task sets did not affect learning. Long-term stability of trained controllers was observed. Using human-generated rewards to train RL controllers for upper-extremity FES systems may be useful. Our findings represent progress toward achieving human-machine teaming in control of upper-extremity FES systems for more natural arm movements based on human user preferences and RL algorithm learning capabilities.

Many reinforcement learning algorithms use trajectories collected from the execution of one or more policies to propose a new policy. Because execution of a bad policy can be costly or dangerous, techniques for evaluating the performance of the new policy without requiring its execution have been of recent interest in industry. Such off-policy evaluation methods, which estimate the performance of a policy using trajectories collected from the execution of other policies, heretofore have not provided confidences regarding the accuracy of their estimates. In this paper we propose an off-policy method for computing a lower confidence bound on the expected return of a policy.

We present a batch reinforcement learning (RL) algorithm that provides probabilistic guarantees about the quality of each policy that it proposes, and which has no hyper-parameter that requires expert tuning. Specifically, the user may select any performance lower-bound and confidence level and our algorithm will ensure that the probability that it returns a policy with performance below the lower bound is at most the specified confidence level. We then propose an incremental algorithm that executes our policy improvement algorithm repeatedly to generate multiple policy improvements. We show the viability of our approach with a simple 4 x 4 gridworld and the standard mountain car problem, as well as with a digital marketing application that uses real world data.

We propose the Ω-return as an alternative to the λ-return currently used by the TD(λ) family of algorithms. The benefit of the Ω-return is that it accounts for the correlation of different length returns. Because it is difficult to compute exactly, we suggest one way of approximating the Ω-return. We provide empirical studies that suggest that it is superior to the λ-return and γ-return for a variety of problems.

In this paper we investigate the application of natural gradient descent to Bellman error based reinforcement learning algorithms. This combination is interesting because natural gradient descent is invariant to the parameterization of the value function. This invariance property means that natural gradient descent adapts its update directions to correct for poorly conditioned representations. We present and analyze quadratic and linear time natural temporal difference learning algorithms, and prove that they are covariant. We conclude with experiments which suggest that the natural algorithms can match or outperform their non-natural counterparts using linear function approximation, and drastically improve upon their non-natural counterparts when using non-linear function approximation.

Natural actor-critics are a popular class of policy search algorithms for finding locally optimal policies for Markov decision processes. In this paper we address a drawback of natural actor-critics that limits their real-world applicability - their lack of safety guarantees. We present a principled algorithm for performing natural gradient descent over a constrained domain. In the context of reinforcement learning, this allows for natural actor-critic algorithms that are guaranteed to remain within a known safe region of policy space. While deriving our class of constrained natural actor-critic algorithms, which we call Projected Natural Actor-Critics (PNACs), we also elucidate the relationship between natural gradient descent and mirror descent.

We describe the Fourier basis, a linear value function approximation scheme based on the Fourier series. We empirically demonstrate that it performs well compared to radial basis functions and the polynomial basis, the two most popular fixed bases for linear value function approximation, and is competitive with learned proto-value functions.

We show that the lambda-return target used in the TD(lambda) family of algorithms is the maximum likelihood estimator for a specific model of how the variance of an n-step return estimate increases with n. We introduce the gamma-return estimator, an alternative target based on a more accurate model of variance, which defines the TDgamma family of complex-backup temporal difference learning algorithms. We derive TDgamma, the gamma-return equivalent of the original TD(lambda) algorithm, which eliminates the lambda parameter but can only perform updates at the end of an episode and requires time and space proportional to the episode length. We then derive a second algorithm, TDgamma(C), with a capacity parameter C. TDgamma(C) requires C times more time and memory than TD(lambda) and is incremental and online. We show that TDgamma outperforms TD(lambda) for any setting of lambda on 4 out of 5 benchmark domains, and that TDgamma(C) performs as well as or better than TD_gamma for intermediate settings of C.

We present a novel class of actor-critic algorithms for actors consisting of sets of interacting modules. We present, analyze theoretically, and empirically evaluate an update rule for each module, which requires only local information: the module's input, output, and the TD error broadcast by a critic. Such updates are necessary when computation of compatible features becomes prohibitively difficult and are also desirable to increase the biological plausibility of reinforcement learning methods.