Deep reinforcement learning (RL) works impressively in some environments and fails catastrophically in others. Ideally, RL theory should be able to provide an understanding of why this is, i.e. bounds predictive of practical performance. Unfortunately, current theory does not quite have this ability. We compare standard deep RL algorithms to prior sample complexity bounds by introducing a new dataset, BRIDGE. It consists of 155 deterministic MDPs from common deep RL benchmarks, along with their corresponding tabular representations, which enables us to exactly compute instance-dependent bounds. We choose to focus on deterministic environments because they share many interesting properties of stochastic environments, but are easier to analyze. Using BRIDGE, we find that prior bounds do not correlate well with when deep RL succeeds vs. fails, but discover a surprising property that does. When actions with the highest Q-values under the random policy also have the highest Q-values under the optimal policy (i.e. when it is optimal to be greedy on the random policy's Q function), deep RL tends to succeed; when they don't, deep RL tends to fail. We generalize this property into a new complexity measure of an MDP that we call the effective horizon, which roughly corresponds to how many steps of lookahead search would be needed in that MDP in order to identify the next optimal action, when leaf nodes are evaluated with random rollouts. Using BRIDGE, we show that the effective horizon-based bounds are more closely reflective of the empirical performance of PPO and DQN than prior sample complexity bounds across four metrics. We also find that, unlike existing bounds, the effective horizon can predict the effects of using reward shaping or a pre-trained exploration policy. Our code and data are available at https://github.com/cassidylaidlaw/effective-horizon

We study reinforcement learning (RL) with linear function approximation. For episodic time-inhomogeneous linear Markov decision processes (linear MDPs) whose transition probability can be parameterized as a linear function of a given feature mapping, we propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $\tilde O(d\sqrt{H^3K})$, where $d$ is the dimension of the feature mapping, $H$ is the planning horizon, and $K$ is the number of episodes. Our algorithm is based on a weighted linear regression scheme with a carefully designed weight, which depends on a new variance estimator that (1) directly estimates the variance of the optimal value function, (2) monotonically decreases with respect to the number of episodes to ensure a better estimation accuracy, and (3) uses a rare-switching policy to update the value function estimator to control the complexity of the estimated value function class. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.

Model-based reinforcement learning (MBRL) has gained much attention for its ability to learn complex behaviors in a sample-efficient way: planning actions by generating imaginary trajectories with predicted rewards. Despite its success, we found that surprisingly, reward prediction is often a bottleneck of MBRL, especially for sparse rewards that are challenging (or even ambiguous) to predict. Motivated by the intuition that humans can learn from rough reward estimates, we propose a simple yet effective reward smoothing approach, DreamSmooth, which learns to predict a temporally-smoothed reward, instead of the exact reward at the given timestep. We empirically show that DreamSmooth achieves state-of-the-art performance on long-horizon sparse-reward tasks both in sample efficiency and final performance without losing performance on common benchmarks, such as Deepmind Control Suite and Atari benchmarks.

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications, which are analogous to behaviors and requirements in system design and give us the means to verify and synthesize system behaviors with formal guarantees. This monograph provides a survey of the current state of the art on applications of formal methods in the autonomous systems domain. We consider correct-by-construction synthesis under various formulations, including closed systems, reactive, and probabilistic settings. Beyond synthesizing systems in known environments, we address the concept of uncertainty and bound the behavior of systems that employ learning using formal methods. Further, we examine the synthesis of systems with monitoring, a mitigation technique for ensuring that once a system deviates from expected behavior, it knows a way of returning to normalcy. We also show how to overcome some limitations of formal methods themselves with learning. We conclude with future directions for formal methods in reinforcement learning, uncertainty, privacy, explainability of formal methods, and regulation and certification.

Task-oriented dialogue systems (TDSs) are assessed mainly in an offline setting or through human evaluation. The evaluation is often limited to single-turn or is very time-intensive. As an alternative, user simulators that mimic user behavior allow us to consider a broad set of user goals to generate human-like conversations for simulated evaluation. Employing existing user simulators to evaluate TDSs is challenging as user simulators are primarily designed to optimize dialogue policies for TDSs and have limited evaluation capabilities. Moreover, the evaluation of user simulators is an open challenge. In this work, we propose a metaphorical user simulator for end-to-end TDS evaluation, where we define a simulator to be metaphorical if it simulates user's analogical thinking in interactions with systems. We also propose a tester-based evaluation framework to generate variants, i.e., dialogue systems with different capabilities. Our user simulator constructs a metaphorical user model that assists the simulator in reasoning by referring to prior knowledge when encountering new items. We estimate the quality of simulators by checking the simulated interactions between simulators and variants. Our experiments are conducted using three TDS datasets. The proposed user simulator demonstrates better consistency with manual evaluation than an agenda-based simulator and a seq2seq model on three datasets; our tester framework demonstrates efficiency and has been tested on multiple tasks, such as conversational recommendation and e-commerce dialogues.

We propose an incomplete algorithm for Maximum Satisfiability (MaxSAT) specifically designed to run on neural network accelerators such as GPUs and TPUs. Given a MaxSAT problem instance in conjunctive normal form, our procedure constructs a Restricted Boltzmann Machine (RBM) with an equilibrium distribution wherein the probability of a Boolean assignment is exponential in the number of clauses it satisfies. Block Gibbs sampling is used to stochastically search the space of assignments with parallel Markov chains. Since matrix multiplication is the main computational primitive for block Gibbs sampling in an RBM, our approach leads to an elegantly simple algorithm (40 lines of JAX) well-suited for neural network accelerators. Theoretical results about RBMs guarantee that the required number of visible and hidden units of the RBM scale only linearly with the number of variables and constant-sized clauses in the MaxSAT instance, ensuring that the computational cost of a Gibbs step scales reasonably with the instance size. Search throughput can be increased by batching parallel chains within a single accelerator as well as by distributing them across multiple accelerators. As a further enhancement, a heuristic based on unit propagation running on CPU is periodically applied to the sampled assignments. Our approach, which we term RbmSAT, is a new design point in the algorithm-hardware co-design space for MaxSAT. We present timed results on a subset of problem instances from the annual MaxSAT Evaluation's Incomplete Unweighted Track for the years 2018 to 2021. When allotted the same running time and CPU compute budget (but no TPUs), RbmSAT outperforms other participating solvers on problems drawn from three out of the four years' competitions. Given the same running time on a TPU cluster for which RbmSAT is uniquely designed, it outperforms all solvers on problems drawn from all four years.

A stochastic process that arises by composing a function with a Markov process is called an aggregated Markov process (AMP). The purpose of composing a Markov process with a function can be a reduction of dimensions, e.g., a projection onto certain coordinates. The theory around AMP has been extensively studied e.g. by Dynkin, Cameron, Rogers and Pitman, and Kelly, all of whom provided sufficient conditions for an AMP to remain Markov. In another direction, Larget provided a canonical representation for AMP, which can be used to verify the equivalence of two AMPs. The purpose of this paper is to describe how the theory of AMP can be applied to stochastic learning theory as they learn a particular task.

Mobile health aims to enhance health outcomes by delivering interventions to individuals as they go about their daily life. The involvement of care partners and social support networks often proves crucial in helping individuals managing burdensome medical conditions. This presents opportunities in mobile health to design interventions that target the dyadic relationship -- the relationship between a target person and their care partner -- with the aim of enhancing social support. In this paper, we develop dyadic RL, an online reinforcement learning algorithm designed to personalize intervention delivery based on contextual factors and past responses of a target person and their care partner. Here, multiple sets of interventions impact the dyad across multiple time intervals. The developed dyadic RL is Bayesian and hierarchical. We formally introduce the problem setup, develop dyadic RL and establish a regret bound. We demonstrate dyadic RL's empirical performance through simulation studies on both toy scenarios and on a realistic test bed constructed from data collected in a mobile health study.

What are the functionals of the reward that can be computed and optimized exactly in Markov Decision Processes? In the finite-horizon, undiscounted setting, Dynamic Programming (DP) can only handle these operations efficiently for certain classes of statistics. We summarize the characterization of these classes for policy evaluation, and give a new answer for the planning problem. Interestingly, we prove that only generalized means can be optimized exactly, even in the more general framework of Distributional Reinforcement Learning (DistRL). DistRL permits, however, to evaluate other functionals approximately. We provide error bounds on the resulting estimators, and discuss the potential of this approach as well as its limitations. These results contribute to advancing the theory of Markov Decision Processes by examining overall characteristics of the return, and particularly risk-conscious strategies.

Several recent works have proposed instance-dependent upper bounds on the number of episodes needed to identify, with probability $1-\delta$, an $\varepsilon$-optimal policy in finite-horizon tabular Markov Decision Processes (MDPs). These upper bounds feature various complexity measures for the MDP, which are defined based on different notions of sub-optimality gaps. However, as of now, no lower bound has been established to assess the optimality of any of these complexity measures, except for the special case of MDPs with deterministic transitions. In this paper, we propose the first instance-dependent lower bound on the sample complexity required for the PAC identification of a near-optimal policy in any tabular episodic MDP. Additionally, we demonstrate that the sample complexity of the PEDEL algorithm of \cite{Wagenmaker22linearMDP} closely approaches this lower bound. Considering the intractability of PEDEL, we formulate an open question regarding the possibility of achieving our lower bound using a computationally-efficient algorithm.