Many interesting real world domains involve reinforcement learning (RL) in partially observable environments. Efficient learning in such domains is important, but existing sample complexity bounds for partially observable RL are at least exponential in the episode length. We give, to our knowledge, the first partially observable RL algorithm with a polynomial bound on the number of episodes on which the algorithm may not achieve near-optimal performance. Our algorithm is suitable for an important class of episodic POMDPs. Our approach builds on recent advances in method of moments for latent variable model estimation.
In reinforcement learning, agents have successfully used environments modeled with Markov decision processes (MDPs). However, in many problem domains, an agent may suffer from noisy observations or random times until its subsequent decision. While partially observable Markov decision processes (POMDPs) have dealt with noisy observations, they have yet to deal with the unknown time aspect. Of course, one could discretize the time, but this leads to Bellman's Curse of Dimensionality. To incorporate continuous sojourn-time distributions in the agent's decision making, we propose that partially ob…
Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms called Uniform-PAC, which is a strengthening of the classical Probably Approximately Correct (PAC) framework. In contrast to the PAC framework, the uniform version may be used to derive high probability regret guarantees and so forms a bridge between the two setups that has been missing in the literature. We demonstrate the benefits of the new framework for fin…
University of California, Irvine（加州大学欧文分校）；The George Washington University（乔治华盛顿大学）
We study the problem of off-policy evaluation (OPE) for episodic Partially Observable Markov Decision Processes (POMDPs) with continuous states. Motivated by the recently proposed proximal causal inference framework, we develop a non-parametric identification result for estimating the policy value via a sequence of so-called V-bridge functions with the help of time-dependent proxy variables. We then develop a fitted-Q-evaluation-type algorithm to estimate V-bridge functions recursively, where a non-parametric instrumental variable (NPIV) problem is solved at each step. By analyzing this challe…
Princeton University（普林斯顿大学）；University of Washington（华盛顿大学）；Microsoft Research, NYC（微软研究院纽约分院）
Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number of computational and statistical hardness results for learning general Partially Observable Markov Decision Processes (POMDPs). This work shows that these hardness barriers do not preclude efficient reinforcement learning for rich and interesting subclasses of POMDPs. In particular, we present a sample-efficient algorithm, OOM-UCB, for episodic finite under…
POMDPPlanners: Open-Source Package for POMDP Planning
Faculty of Mathematics Technion - Israel Institute of Technology（数学系技术学院 - 以色列理工学院）；Stephen B. Klein Faculty of Aerospace Engineering Faculty of Data and Decision Sciences Technion - Israel Institute of Technology（Stephen B. Klein航空航天工程系数据与决策科学系技术学院 - 以色列理工学院）
We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action $Q$-function is linear in the state feature, and the optima…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of …
In this paper, we propose new problem-independent lower bounds on the sample complexity and regret in episodic MDPs, with a particular focus on the non-stationary case in which the transition kernel is allowed to change in each stage of the episode. Our main contribution is a novel lower bound of $Ω((H^3SA/ε^2)\log(1/δ))$ on the sample complexity of an $(\varepsilon,δ)$-PAC algorithm for best policy identification in a non-stationary MDP. This lower bound relies on a construction of "hard MDPs" which is different from the ones previously used in the literature. Using this same class of MDPs, w…
In this paper we study online Reinforcement Learning (RL) in partially observable dynamical systems. We focus on the Predictive State Representations (PSRs) model, which is an expressive model that captures other well-known models such as Partially Observable Markov Decision Processes (POMDP). PSR represents the states using a set of predictions of future observations and is defined entirely using observable quantities. We develop a novel model-based algorithm for PSRs that can learn a near optimal policy in sample complexity scaling polynomially with respect to all the relevant parameters of …
This paper studies the fundamental limits of reinforcement learning (RL) in the challenging \emph{partially observable} setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires exponentially many samples in the worst case, a surge of recent work shows that polynomial sample complexities are achievable under the \emph{revealing condition} -- A natural condition that requires the observables to reveal some information about the unobserved latent states. However, the fundamental limits for learning in revealing POMDPs are much less un…
Missingness-MDPs: Bridging the Theory of Missing Data and POMDPs
Ruhr University Bochum（博德姆鲁尔大学）；Brno University of Technology（布拉格技术大学）；Radboud University Nijmegen（拉德博德大学奈杰姆）；Harvard University（哈佛大学）；Eindhoven University of Technology（埃因霍温理工大学）
Meta AI；UMPA, ENS Lyon（里昂高等师范学院纯数学与应用数学实验室）；Univ. Lille（里尔大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Centrale Lille（里尔中央理工学院）
In probably approximately correct (PAC) reinforcement learning (RL), an agent is required to identify an $ε$-optimal policy with probability $1-δ$. While minimax optimal algorithms exist for this problem, its instance-dependent complexity remains elusive in episodic Markov decision processes (MDPs). In this paper, we propose the first nearly matching (up to a horizon squared factor and logarithmic terms) upper and lower bounds on the sample complexity of PAC RL in deterministic episodic MDPs with finite state and action spaces. In particular, our bounds feature a new notion of sub-optimality g…
Optimal decision making with limited or no information in stochastic environments where multiple agents interact is a challenging topic in the realm of artificial intelligence. Reinforcement learning (RL) is a popular approach for arriving at optimal strategies by predicating stimuli, such as the reward for following a strategy, on experience. RL is heavily explored in the single-agent context, but is a nascent concept in multiagent problems. To this end, I propose several principled model-free and partially model-based reinforcement learning approaches for several multiagent settings. In the …
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 finite-horizon CMDP for repeated optimistic planning to provide a probably approximately correct (PAC) guarantee on the number of episodes needed to ensure an $ε$-optimal policy, i.e., with resulting objective value within $ε$ of the optimal value …
Our work aims at developing reinforcement learning algorithms that do not rely on the Markov assumption. We consider the class of Non-Markov Decision Processes where histories can be abstracted into a finite set of states while preserving the dynamics. We call it a Markov abstraction since it induces a Markov Decision Process over a set of states that encode the non-Markov dynamics. This phenomenon underlies the recently introduced Regular Decision Processes (as well as POMDPs where only a finite number of belief states is reachable). In all such kinds of decision process, an agent that uses a…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）；Microsoft Research（微软研究院）
We propose and study a new model for reinforcement learning with rich observations, generalizing contextual bandits to sequential decision making. These models require an agent to take actions based on observations (features) with the goal of achieving long-term performance competitive with a large set of policies. To avoid barriers to sample-efficient learning associated with large observation spaces and general POMDPs, we focus on problems that can be summarized by a small number of hidden states and have long-term rewards that are predictable by a reactive function class. In this setting, w…
University of Minnesota（明尼苏达大学）；DeepMind；Microsoft Research（微软研究院）；Carnegie Mellon University（卡内基梅隆大学）
Motivated by high-stakes decision-making domains like personalized medicine where user information is inherently sensitive, we design privacy preserving exploration policies for episodic reinforcement learning (RL). We first provide a meaningful privacy formulation using the notion of joint differential privacy (JDP)--a strong variant of differential privacy for settings where each user receives their own sets of output (e.g., policy recommendations). We then develop a private optimism-based learning algorithm that simultaneously achieves strong PAC and regret bounds, and enjoys a JDP guarante…
The focus of this paper is on solving multi-robot planning problems in continuous spaces with partial observability. Decentralized partially observable Markov decision processes (Dec-POMDPs) are general models for multi-robot coordination problems, but representing and solving Dec-POMDPs is often intractable for large problems. To allow for a high-level representation that is natural for multi-robot problems and scalable to large discrete and continuous problems, this paper extends the Dec-POMDP model to the decentralized partially observable semi-Markov decision process (Dec-POSMDP). The Dec-…
Univ. of Michigan（密歇根大学）；Microsoft Research（微软研究院）
We consider a reinforcement learning (RL) setting in which the agent interacts with a sequence of episodic MDPs. At the start of each episode the agent has access to some side-information or context that determines the dynamics of the MDP for that episode. Our setting is motivated by applications in healthcare where baseline measurements of a patient at the start of a treatment episode form the context that may provide information about how the patient might respond to treatment decisions. We propose algorithms for learning in such Contextual Markov Decision Processes (CMDPs) under an assumpti…
Stanford University（斯坦福大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；UC Santa Barbara（加州大学圣巴巴拉分校）
We take initial steps in studying PAC-MDP algorithms with limited adaptivity, that is, algorithms that change its exploration policy as infrequently as possible during regret minimization. This is motivated by the difficulty of running fully adaptive algorithms in real-world applications (such as medical domains), and we propose to quantify adaptivity using the notion of local switching cost. Our main contribution, Q-Learning with UCB2 exploration, is a model-free algorithm for H-step episodic MDP that achieves sublinear regret whose local switching cost in K episodes is $O(H^3SA\log K)$, and …
This paper proposes an intent-aware multi-agent planning framework as well as a learning algorithm. Under this framework, an agent plans in the goal space to maximize the expected utility. The planning process takes the belief of other agents' intents into consideration. Instead of formulating the learning problem as a partially observable Markov decision process (POMDP), we propose a simple but effective linear function approximation of the utility function. It is based on the observation that for humans, other people's intents will pose an influence on our utility for a goal. The proposed fr…
Meta AI；ENS Lyon（里昂高等师范学院）；Univ. Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）
Optimistic algorithms have been extensively studied for regret minimization in episodic tabular MDPs, both from a minimax and an instance-dependent view. However, for the PAC RL problem, where the goal is to identify a near-optimal policy with high probability, little is known about their instance-dependent sample complexity. A negative result of Wagenmaker et al. (2021) suggests that optimistic sampling rules cannot be used to attain the (still elusive) optimal instance-dependent sample complexity. On the positive side, we provide the first instance-dependent bound for an optimistic algorithm…
Wesleyan University（卫斯理大学）；University of Connecticut（康涅狄格大学）；Fordham University（福特汉姆大学）
While routing in wireless networks has been studied extensively, existing protocols are typically designed for a specific set of network conditions and so cannot accommodate any drastic changes in those conditions. For instance, protocols designed for connected networks cannot be easily applied to disconnected networks. In this paper, we develop a distributed routing strategy based on deep reinforcement learning that generalizes to diverse traffic patterns, congestion levels, network connectivity, and link dynamics. We make the following key innovations in our design: (i) the use of relational…
Nanjing University of Science and Technology（南京理工大学）；CSIRO（澳大利亚联邦科学与工业研究组织）；Shanghai Jiao Tong University（上海交通大学）；Southeast University（东南大学）
The explosive growth of dynamic and heterogeneous data traffic brings great challenges for 5G and beyond mobile networks. To enhance the network capacity and reliability, we propose a learning-based dynamic time-frequency division duplexing (D-TFDD) scheme that adaptively allocates the uplink and downlink time-frequency resources of base stations (BSs) to meet the asymmetric and heterogeneous traffic demands while alleviating the inter-cell interference. We formulate the problem as a decentralized partially observable Markov decision process (Dec-POMDP) that maximizes the long-term expected su…
UC Berkeley（加州大学伯克利分校）；Columbia University（哥伦比亚大学）；Microsoft Research NYC（微软研究院纽约）；Massachusetts Institute of Technology（麻省理工学院）
Thompson sampling and other Bayesian sequential decision-making algorithms are among the most popular approaches to tackle explore/exploit trade-offs in (contextual) bandits. The choice of prior in these algorithms offers flexibility to encode domain knowledge but can also lead to poor performance when misspecified. In this paper, we demonstrate that performance degrades gracefully with misspecification. We prove that the expected reward accrued by Thompson sampling (TS) with a misspecified prior differs by at most $\tilde{\mathcal{O}}(H^2 ε)$ from TS with a well specified prior, where $ε$ is …
