Various algorithms for reinforcement learning (RL) exhibit dramatic variation in their convergence rates as a function of problem structure. Such problem-dependent behavior is not captured by worst-case analyses and has accordingly inspired a growing effort in obtaining instance-dependent guarantees and deriving instance-optimal algorithms for RL problems. This research has been carried out, however, primarily within the confines of theory, providing guarantees that explain \textit{ex post} the performance differences observed. A natural next step is to convert these theoretical guarantees into guidelines that are useful in practice. We address the problem of obtaining sharp instance-dependent confidence regions for the policy evaluation problem and the optimal value estimation problem of an MDP, given access to an instance-optimal algorithm. As a consequence, we propose a data-dependent stopping rule for instance-optimal algorithms. The proposed stopping rule adapts to the instance-specific difficulty of the problem and allows for early termination for problems with favorable structure.
This paper presents an inverse reinforcement learning~(IRL) framework for Bayesian stopping time problems. By observing the actions of a Bayesian decision maker, we provide a necessary and sufficient condition to identify if these actions are consistent with optimizing a cost function. In a Bayesian (partially observed) setting, the inverse learner can at best identify optimality wrt the observed strategies. Our IRL algorithm identifies optimality and then constructs set-valued estimates of the cost function.To achieve this IRL objective, we use novel ideas from Bayesian revealed preferences s…
Department of Electrical & Computer Engineering University of Washington（华盛顿大学电气与计算机工程系）
Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for settings in which the reward function and the constraints, described by cost functions, are unknown a priori but the transition kernel is known. Such a setting is well-motivated by a number of applications including exploration of unknown, potentially unsafe, environments. We present an algorithm C-UCRL and show that it achieves sub-linear regret ($ O(T^{\frac{…
We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments…
Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 - CRIStAL（里尔大学、法国国家科学研究中心、法国国家信息与自动化研究所、里尔中央理工学院、UMR 9189 - CRIStAL实验室）；Centrum Wiskunde & Informatica（荷兰数学与计算机科学研究中心）
This paper presents new deviation inequalities that are valid uniformly in time under adaptive sampling in a multi-armed bandit model. The deviations are measured using the Kullback-Leibler divergence in a given one-dimensional exponential family, and may take into account several arms at a time. They are obtained by constructing for each arm a mixture martingale based on a hierarchical prior, and by multiplying those martingales. Our deviation inequalities allow us to analyze stopping rules based on generalized likelihood ratios for a large class of sequential identification problems, and to …
We develop confidence bounds that hold uniformly over time for off-policy evaluation in the contextual bandit setting. These confidence sequences are based on recent ideas from martingale analysis and are non-asymptotic, non-parametric, and valid at arbitrary stopping times. We provide algorithms for computing these confidence sequences that strike a good balance between computational and statistical efficiency. We empirically demonstrate the tightness of our approach in terms of failure probability and width and apply it to the "gated deployment" problem of safely upgrading a production conte…
University of Pennsylvania（宾夕法尼亚大学）；Nokia Bell Labs（诺基亚贝尔实验室）
We study regenerative stopping problems in which the system starts anew whenever the controller decides to stop and the long-term average cost is to be minimized. Traditional model-based solutions involve estimating the underlying process from data and computing strategies for the estimated model. In this paper, we compare such solutions to deep reinforcement learning and imitation learning which involve learning a neural network policy from simulations. We evaluate the different approaches on a real-world problem of shipping consolidation in logistics and demonstrate that deep learning can be…
Inria Lille Nord Europe（法国国家信息与自动化研究所里尔-北欧中心）；Université de Lille（里尔大学）；Leiden University（莱顿大学）；CWI（荷兰数学与信息学研究中心）；CNRS（法国国家科学研究中心）；DeepMind Paris（DeepMind巴黎）
We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our main contribution, we provide the first sample complexity analysis of TTTS and T3C when coupled with a very natural Bayesian stopping rule, for bandits with Gaussian rewards, solving one of the open questions raised by Russo (2016). We also provide new posterior convergence resul…
We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under drifting non-stationarity, i.e., both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning with Confidence Widening (SWUCRL2-CW) algorithm, and establish its dynamic regret bound when the variation budgets are known. In addition, we propose the Bandit-over-Reinforcement Le…
KTH Royal Institute of Technology（瑞典皇家理工学院）；KTH Center for Cyber Defense and Information Security（KTH网络防御与信息安全中心）
We study automated intrusion prevention using reinforcement learning. Following a novel approach, we formulate the interaction between an attacker and a defender as an optimal stopping game and let attack and defense strategies evolve through reinforcement learning and self-play. The game-theoretic perspective allows us to find defender strategies that are effective against dynamic attackers. The optimal stopping formulation gives us insight into the structure of optimal strategies, which we show to have threshold properties. To obtain the optimal defender strategies, we introduce T-FP, a fict…
In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance bounds in the inverse reinforcement learning setting---where the true reward function is unknown and only samples of expert behavior are given. We propose a sampling method based on Bayesian inverse reinforcement learning that uses demonstrations to determine practical high-confidence upper bounds on the $α$-worst-case difference in expected return between a…
University of Michigan（密歇根大学）；University of Southern California（南加州大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）
We consider online learning for episodic stochastically constrained Markov decision processes (CMDPs), which plays a central role in ensuring the safety of reinforcement learning. Here the loss function can vary arbitrarily across the episodes, and both the loss received and the budget consumption are revealed at the end of each episode. Previous works solve this problem under the restrictive assumption that the transition model of the Markov decision processes (MDPs) is known a priori and establish regret bounds that depend polynomially on the cardinalities of the state space $\mathcal{S}$ an…
On the effectiveness of reward functions in reinforcement learning for confidence calibration of large language models
School of Computing National University of Singapore（新加坡国立大学计算机学院）；Institute of Advanced Intelligence and Computing（高级智能与计算研究所）；Agency for Science, Technology and Research（科技研究局）；Department of Electrical & Computer Engineering（电气与计算机工程系）
Active learning from demonstration allows a robot to query a human for specific types of input to achieve efficient learning. Existing work has explored a variety of active query strategies; however, to our knowledge, none of these strategies directly minimize the performance risk of the policy the robot is learning. Utilizing recent advances in performance bounds for inverse reinforcement learning, we propose a risk-aware active inverse reinforcement learning algorithm that focuses active queries on areas of the state space with the potential for large generalization error. We show that risk-…
Vector Institute for Artificial Intelligence（向量人工智能研究所）；School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）；Huawei Technologies Canada（华为技术加拿大公司）；Cheriton School of Computer Science, University of Waterloo（滑铁卢大学谢里敦计算机科学学院）
Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence intervals that are valid uniformly over the growing-into-infinity sample sizes. To address this question, we provide a near-optimal confidence sequence for bounded random variables by utilizing Bentkus' concentration results. We show that it improves on the existing approaches that use the Cram{é}r-Chernoff technique such as the Hoeffding, Bernstein, and Be…
Estimating the value function for a fixed policy is a fundamental problem in reinforcement learning. Policy evaluation algorithms---to estimate value functions---continue to be developed, to improve convergence rates, improve stability and handle variability, particularly for off-policy learning. To understand the properties of these algorithms, the experimenter needs high-confidence estimates of the accuracy of the learned value functions. For environments with small, finite state-spaces, like chains, the true value function can be easily computed, to compute accuracy. For large, or continuou…
National University of Singapore（新加坡国立大学）；Massachusetts Institute of Technology（麻省理工学院）
We consider un-discounted reinforcement learning (RL) in Markov decision processes (MDPs) under temporal drifts, ie, both the reward and state transition distributions are allowed to evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain variation budgets. This setting captures the endogeneity, exogeneity, uncertainty, and partial feedback in sequential decision-making scenarios, and finds applications in vehicle remarketing and real-time bidding. We first develop the Sliding Window Upper-Confidence bound for Reinforcement Learning…
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）；UPS IMT（图卢兹第三大学国立图卢兹应用科学学院）；Univ. Lille（里尔大学）；CRIStAL - Centre de Recherche en Informatique Signal et Automatique de Lille（里尔计算机、信号与自动化研究中心）；Inria（法国国家信息与自动化研究所）
We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optimal proportions of arm draws highlighted by the lower bound) and in a stopping rule named after Chernoff, for which we give a new analysis.
University of Freiburg（弗莱堡大学）；University of Technology Nuremberg（纽伦堡工业大学）
Early stopping based on the validation set performance is a popular approach to find the right balance between under- and overfitting in the context of supervised learning. However, in reinforcement learning, even for supervised sub-problems such as world model learning, early stopping is not applicable as the dataset is continually evolving. As a solution, we propose a new general method that dynamically adjusts the update to data (UTD) ratio during training based on under- and overfitting detection on a small subset of the continuously collected experience not used for training. We apply our…
Meta AI；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）
Elimination algorithms for bandit identification, which prune the plausible correct answers sequentially until only one remains, are computationally convenient since they reduce the problem size over time. However, existing elimination strategies are often not fully adaptive (they update their sampling rule infrequently) and are not easy to extend to combinatorial settings, where the set of answers is exponentially large in the problem dimension. On the other hand, most existing fully-adaptive strategies to tackle general identification problems are computationally demanding since they repeate…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Princeton University（普林斯顿大学）
The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be improved in the sense that the number of samples required to identify the best arm is within a constant factor of a lower bound based on the law of the iterated logarithm (LIL). Inspired by the LIL, we construct our confidence bounds to explicitly account for the infinite time horizon of the algorithm. In addition, by using a novel stopping time for the algorith…
Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the $p$-th central moment ($p$ > 1), but allowing for (at most) $ε$ fraction of arbitrary distribution corruption, as in Huber's contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisi…
Technical University of Munich（慕尼黑工业大学）；ETH Zurich（苏黎世联邦理工学院）
Ensuring safety is a crucial challenge when deploying reinforcement learning (RL) to real-world systems. We develop confidence-based safety filters, a control-theoretic approach for certifying state safety constraints for nominal policies learned via standard RL techniques, based on probabilistic dynamics models. Our approach is based on a reformulation of state constraints in terms of cost functions, reducing safety verification to a standard RL task. By exploiting the concept of hallucinating inputs, we extend this formulation to determine a "backup" policy that is safe for the unknown syste…
Model-based Bootstrap for Offline Policy Evaluation in Tabular Reinforcement Learning
Southern University of Science and Technology（南方科技大学）；East China Normal University（华东师范大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Loop Area Institute（深圳河套学院）
Inria Lille – Nord Europe（法国国家信息与自动化研究所里尔-北欧洲研究中心）；University of Copenhagen（哥本哈根大学）
The upper confidence reinforcement learning (UCRL2) algorithm introduced in (Jaksch et al., 2010) is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this algorithm and its variants have remained until now mostly theoretical as numerical experiments in simple environments exhibit long burn-in phases before the learning takes place. In pursuit of practical efficiency, we present UCRL3, following the lines of UCRL2, but with two key modifications: First, it…
University of Alberta（阿尔伯塔大学）；DeepMind（深度思维）；Google Research（谷歌研究院）
We study high-confidence behavior-agnostic off-policy evaluation in reinforcement learning, where the goal is to estimate a confidence interval on a target policy's value, given only access to a static experience dataset collected by unknown behavior policies. Starting from a function space embedding of the linear program formulation of the $Q$-function, we obtain an optimization problem with generalized estimating equation constraints. By applying the generalized empirical likelihood method to the resulting Lagrangian, we propose CoinDICE, a novel and efficient algorithm for computing confide…
Beijing University of Posts and Telecommunications（北京邮电大学）；China Electric Power Research Institute（中国电力科学研究院）
The expansion of renewable energy could help realizing the goals of peaking carbon dioxide emissions and carbon neutralization. Some existing grid dispatching methods integrating short-term renewable energy prediction and reinforcement learning (RL) have been proved to alleviate the adverse impact of energy fluctuations risk. However, these methods omit the long-term output prediction, which leads to stability and security problems on the optimal power flow. This paper proposes a confidence estimation Transformer for long-term renewable energy forecasting in reinforcement learning-based power …
Offline reinforcement learning algorithms still lack trust in practice due to the risk that the learned policy performs worse than the original policy that generated the dataset or behaves in an unexpected way that is unfamiliar to the user. At the same time, offline RL algorithms are not able to tune their most important hyperparameter - the proximity of the learned policy to the original policy. We propose an algorithm that allows the user to tune this hyperparameter at runtime, thereby addressing both of the above mentioned issues simultaneously. This allows users to start with the original…
University of California, San Diego（加州大学圣地亚哥分校）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Rewards and punishments in different forms are pervasive and present in a wide variety of decision-making scenarios. By observing the outcome of a sufficient number of repeated trials, one would gradually learn the value and usefulness of a particular policy or strategy. However, in a given environment, the outcomes resulting from different trials are subject to chance influence and variations. In learning about the usefulness of a given policy, significant costs are involved in systematically undertaking the sequential trials; therefore, in most learning episodes, one would wish to keep the c…
NVIDIA Research（英伟达研究院）；Technion - Israel Institute of Technology（以色列理工学院）；Indian Institute of Technology, Indore（印度理工学院印多尔分校）
In recent years, there has been significant progress in applying deep reinforcement learning (RL) for solving challenging problems across a wide variety of domains. Nevertheless, convergence of various methods has been shown to suffer from inconsistencies, due to algorithmic instability and variance, as well as stochasticity in the benchmark environments. Particularly, despite the fact that the agent's performance may be improving on average, it may abruptly deteriorate at late stages of training. In this work, we study methods for enhancing the agent's learning process, by providing conservat…
Ranking-Aware Calibration for Reliable Multimodal Reinforcement Learning
Dept. of Comp. Sci. & Tech., Institute for AI, BNRist Center, Tsinghua-Bosch Joint ML Center, THBI Lab, Tsinghua University, Beijing（计算机科学与技术系，人工智能研究院，BNRist中心，清华大学-博世联合机器学习中心，THBI实验室，清华大学，北京）；Dept. of Automation, Tsinghua University, Beijing（自动化系，清华大学，北京）
Beijing National Laboratory for Molecular Sciences (BNLMS)（北京分子科学国家实验室）
Most algorithms for the multi-armed bandit problem in reinforcement learning aimed to maximize the expected reward, which are thus useful in searching the optimized candidate with the highest reward (function value) for diverse applications (e.g., AlphaGo). However, in some typical application scenaios such as drug discovery, the aim is to search a diverse set of candidates with high reward. Here we propose a reversible upper confidence bound (rUCB) algorithm for such a purpose, and demonstrate its application in virtual screening upon intrinsically disordered proteins (IDPs). It is shown that…
