We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic approximation scheme, and establish non-asymptotic bounds for both the operator defect and the estimation error, measured in an arbitrary semi-norm. In contrast to worst-case guarantees, our bounds are instance-dependent, and achieve the local asymptotic minimax risk non-asymptotically. For linear operators, contractivity can be relaxed to multi-step contractivity, so that the theory can be applied to problems like average reward policy evaluation problem in reinforcement learning. We illustrate the theory via applications to stochastic shortest path problems, two-player zero-sum Markov games, as well as policy evaluation and $Q$-learning for tabular Markov decision processes.

Assessing the effects of a policy based on observational data from a different policy is a common problem across several high-stake decision-making domains, and several off-policy evaluation (OPE) techniques have been proposed. However, these methods largely formulate OPE as a problem disassociated from the process used to generate the data (i.e. structural assumptions in the form of a causal graph). We argue that explicitly highlighting this association has important implications on our understanding of the fundamental limits of OPE. First, this implies that current formulation of OPE corresponds to a narrow set of tasks, i.e. a specific causal estimand which is focused on prospective evaluation of policies over populations or sub-populations. Second, we demonstrate how this association motivates natural desiderata to consider a general set of causal estimands, particularly extending the role of OPE for counterfactual off-policy evaluation at the level of individuals of the population. A precise description of the causal estimand highlights which OPE estimands are identifiable from observational data under the stated generative assumptions. For those OPE estimands that are not identifiable, the causal perspective further highlights where more experimental data is necessary, and highlights situations where human expertise can aid identification and estimation. Furthermore, many formalisms of OPE overlook the role of uncertainty entirely in the estimation process.We demonstrate how specifically characterising the causal estimand highlights the different sources of uncertainty and when human expertise can naturally manage this uncertainty. We discuss each of these aspects as actionable desiderata for future OPE research at scale and in-line with practical utility.

Rishabh Agarwal, Max Schwarzer, Pablo Samuel Castro, Aaron Courville and Marc G. Bellemare won an outstanding paper award at NeurIPS2021 for their paper Deep Reinforcement Learning at the Edge of the Statistical Precipice. In this blog post, Rishabh Agarwal and Pablo Samuel Castro explain this work. Reinforcement learning (RL) is an area of machine learning that focuses on learning from experiences to solve decision making tasks. While the field of RL has made great progress, resulting in impressive empirical results on complex tasks, such as playing video games, flying stratospheric balloons and designing hardware chips, it is becoming increasingly apparent that the current standards for empirical evaluation might give a false sense of fast scientific progress while slowing it down. To that end, in "Deep RL at the Edge of the Statistical Precipice", given as an oral presentation at NeurIPS 2021, we discuss how statistical uncertainty of results needs to be considered, especially when using only a few training runs, in order for evaluation in deep RL to be reliable.

This paper offers a new hybrid probably approximately correct (PAC) reinforcement learning (RL) algorithm for Markov decision processes (MDPs) that intelligently maintains favorable features of both model-based and model-free methodologies. The designed algorithm, referred to as the Dyna-Delayed Q-learning (DDQ) algorithm, combines model-free Delayed Q-learning and model-based R-max algorithms while outperforming both in most cases. The paper includes a PAC analysis of the DDQ algorithm and a derivation of its sample complexity. Numerical results are provided to support the claim regarding the new algorithm's sample efficiency compared to its parents as well as the best-known PAC model-free and model-based algorithms in application. A real-world experimental implementation of DDQ in the context of pediatric motor rehabilitation facilitated by infant-robot interaction highlights the potential benefits of the reported method.

Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task" that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.

In this paper, we focus on the problem of modeling dynamic geo-human interactions in streams for online POI recommendations. Specifically, we formulate the in-stream geo-human interaction modeling problem into a novel deep interactive reinforcement learning framework, where an agent is a recommender and an action is a next POI to visit. We uniquely model the reinforcement learning environment as a joint and connected composition of users and geospatial contexts (POIs, POI categories, functional zones). An event that a user visits a POI in stream updates the states of both users and geospatial contexts; the agent perceives the updated environment state to make online recommendations. Specifically, we model a mixed-user event stream by unifying all users, visits, and geospatial contexts as a dynamic knowledge graph stream, in order to model human-human, geo-human, geo-geo interactions. We design an exit mechanism to address the expired information challenge, devise a meta-path method to address the recommendation candidate generation challenge, and develop a new deep policy network structure to address the varying action space challenge, and, finally, propose an effective adversarial training method for optimization. Finally, we present extensive experiments to demonstrate the enhanced performance of our method.

Behavioural cloning has been extensively used to train agents and is recognized as a fast and solid approach to teach general behaviours based on expert trajectories. Such method follows the supervised learning paradigm and it strongly depends on the distribution of the data. In our paper, we show how combining behavioural cloning with human-in-the-loop training solves some of its flaws and provides an agent task-specific corrections to overcome tricky situations while speeding up the training time and lowering the required resources. To do this, we introduce a novel approach that allows an expert to take control of the agent at any moment during a simulation and provide optimal solutions to its problematic situations. Our experiments show that this approach leads to better policies both in terms of quantitative evaluation and in human-likeliness.

This textbook covers principles behind main modern deep reinforcement learning algorithms that achieved breakthrough results in many domains from game AI to robotics. All required theory is explained with proofs using unified notation and emphasize on the differences between different types of algorithms and the reasons why they are constructed the way they are.

We consider the challenge of finding a deterministic policy for a Markov decision process that uniformly (in all states) maximizes one reward subject to a probabilistic constraint over a different reward. Existing solutions do not fully address our precise problem definition, which nevertheless arises naturally in the context of safety-critical robotic systems. This class of problem is known to be hard, but the combined requirements of determinism and uniform optimality can create learning instability. In this work, after describing and motivating our problem with a simple example, we present a suitable constrained reinforcement learning algorithm that prevents learning instability, using recursive constraints. Our proposed approach admits an approximative form that improves efficiency and is conservative w.r.t. the constraint.

While most reinforcement learning algorithms aim at minimizing the Mean Squared Bellman Error, in function approximation it makes more sense to track the Projected Bellman Error. This is because with function approximation the true optimal of the Bellman Equation might not be representable by the function class. An example would be the true solution not being within the range space of the design matrix when using linear architectures. In such a scenario, one looks at the projected optimal solution onto the range space of the design matrix. This projected optimal solution is the fixed point solution of the Bellman Equation.