Lifelong reinforcement learning provides a promising framework for developing versatile agents that can accumulate knowledge over a lifetime of experience and rapidly learn new tasks by building upon prior knowledge. However, current lifelong learning methods exhibit non-vanishing regret as the amount of experience increases and include limitations that can lead to suboptimal or unsafe control policies. To address these issues, we develop a lifelong policy gradient learner that operates in an adversarial set- ting to learn multiple tasks online while enforcing safety constraints on the learned policies. We demonstrate, for the first time, sublinear regret for lifelong policy search, and validate our algorithm on several benchmark dynamical systems and an application to quadrotor control.
We propose two linear bandits algorithms with per-step complexity sublinear in the number of arms $K$. The algorithms are designed for applications where the arm set is extremely large and slowly changing. Our key realization is that choosing an arm reduces to a maximum inner product search (MIPS) problem, which can be solved approximately without breaking regret guarantees. Existing approximate MIPS solvers run in sublinear time. We extend those solvers and present theoretical guarantees for online learning problems, where adaptivity (i.e., a later step depends on the feedback in previous ste…
University of California, Los Angeles（加州大学洛杉矶分校）；Microsoft Research（微软研究院）
We study lifelong reinforcement learning (RL) in a regret minimization setting of linear contextual Markov decision process (MDP), where the agent needs to learn a multi-task policy while solving a streaming sequence of tasks. We propose an algorithm, called UCB Lifelong Value Distillation (UCBlvd), that provably achieves sublinear regret for any sequence of tasks, which may be adaptively chosen based on the agent's past behaviors. Remarkably, our algorithm uses only sublinear number of planning calls, which means that the agent eventually learns a policy that is near optimal for multiple task…
Centre Borelli, ENS Paris-Saclay（巴黎萨克雷高等师范学院博雷利中心）；Cdiscount（Cdiscount公司）；CREST, ENSAE Paris（巴黎经济与统计高等学校统计与经济研究中心）；Criteo AI Lab（Criteo人工智能实验室）
Continuously learning and leveraging the knowledge accumulated from prior tasks in order to improve future performance is a long standing machine learning problem. In this paper, we study the problem in the multi-armed bandit framework with the objective to minimize the total regret incurred over a series of tasks. While most bandit algorithms are designed to have a low worst-case regret, we examine here the average regret over bandit instances drawn from some prior distribution which may change over time. We specifically focus on confidence interval tuning of UCB algorithms. We propose a band…
The Chinese University of Hong Kong（香港中文大学）；University of Toronto（多伦多大学）
We study the model-based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is the optimal policy of the POMDP with a known environment in terms of the average reward over an infinite horizon. We propose a learning algorithm for this problem, building on spectral method-of-moments estimations for hidden Markov models, the belief error control in POMDPs and upper-confidence-bound methods for online learning. We establish a regret bound of $O(T^{2/3}\sqrt{\log T})$ for the proposed learning algorithm where $T$ is the learning h…
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）；Microsoft Research（微软研究院）
Online learning algorithms are designed to learn even when their input is generated by an adversary. The widely-accepted formal definition of an online algorithm's ability to learn is the game-theoretic notion of regret. We argue that the standard definition of regret becomes inadequate if the adversary is allowed to adapt to the online algorithm's actions. We define the alternative notion of policy regret, which attempts to provide a more meaningful way to measure an online algorithm's performance against adaptive adversaries. Focusing on the online bandit setting, we show that no bandit algo…
An adversarial bandit problem with memory constraints is studied where only the statistics of a subset of arms can be stored. A hierarchical learning policy that requires only a sublinear order of memory space in terms of the number of arms is developed. Its sublinear regret orders with respect to the time horizon are established for both weak regret and shifting regret. This work appears to be the first on memory-constrained bandit problems under the adversarial setting.
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function changes continuously across rounds with respect to the learner's decisions. We show that COL covers and more appropriately describes many interesting applications, from general equilibrium problems (EPs) to optimization in episodic MDPs. In particular, we show monotone EPs admits a …
Isoperimetry is All We Need: Langevin Posterior Sampling for RL with Sublinear Regret
Chalmers University of Technology（查尔姆斯理工大学）；University of Gothenburg（哥德堡大学）；University of Oslo（奥斯陆大学）；Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 – CRIStAL（里尔大学、法国国家信息与自动化研究所、法国国家科学研究中心、里尔中央理工大学、UMR 9189 – CRIStAL）
We derive sublinear regret bounds for undiscounted reinforcement learning in continuous state space. The proposed algorithm combines state aggregation with the use of upper confidence bounds for implementing optimism in the face of uncertainty. Beside the existence of an optimal policy which satisfies the Poisson equation, the only assumptions made are Holder continuity of rewards and transition probabilities.
Massachusetts Institute of Technology（麻省理工学院）；Princeton University（普林斯顿大学）
We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable. We show that in this challenging setting, achieving sublinear regret against the best response in hindsight is statistically hard. We then consider a weaker notion of regret by competing with the \emph{minimax value} of the game, and present an algorithm that achieves a sublinear $\tilde{\mathcal{O}}(K^{2/3})$ regret after $K$ episodes. This is the first sublinear regret bound (to our knowledge) for online learning in unknow…
Revisiting Matrix Sketching in Linear Bandits: Achieving Sublinear Regret via Dyadic Block Sketching
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学人工智能学院）；National Key Laboratory for Novel Software Technology, Nanjing University（南京大学新型软件技术国家重点实验室）
The stochastic multi-armed bandit setting has been recently studied in the non-stationary regime, where the mean payoff of each action is a non-decreasing function of the number of rounds passed since it was last played. This model captures natural behavioral aspects of the users which crucially determine the performance of recommendation platforms, ad placement systems, and more. Even assuming prior knowledge of the mean payoff functions, computing an optimal planning in the above model is NP-hard, while the state-of-the-art is a $1/4$-approximation algorithm for the case where at most one ar…
University of California at Davis（加州大学戴维斯分校）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We study contextual bandits with budget and time constraints, referred to as constrained contextual bandits.The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time.Such coupling effects make it difficult to obtain oracle solutions that assume known statistics of bandits. To gain insight, we first study unit-cost systems with known context distribution. When the expected rewards are known, we develop an approximation of the oracle, referred to Adaptive-Linear-Programming (ALP), which achi…
IIT Bombay（印度理工学院孟买分校）；Boston University（波士顿大学）；University of Alberta（阿尔伯塔大学）
In many security and healthcare systems a sequence of features/sensors/tests are used for detection and diagnosis. Each test outputs a prediction of the latent state, and carries with it inherent costs. Our objective is to {\it learn} strategies for selecting tests to optimize accuracy \& costs. Unfortunately it is often impossible to acquire in-situ ground truth annotations and we are left with the problem of unsupervised sensor selection (USS). We pose USS as a version of stochastic partial monitoring problem with an {\it unusual} reward structure (even noisy annotations are unavailable). Un…
University of California, Berkeley（加州大学伯克利分校）；Indian Institute of Science（印度科学院）
We consider the problem of online learning in misspecified linear stochastic multi-armed bandit problems. Regret guarantees for state-of-the-art linear bandit algorithms such as Optimism in the Face of Uncertainty Linear bandit (OFUL) hold under the assumption that the arms expected rewards are perfectly linear in their features. It is, however, of interest to investigate the impact of potential misspecification in linear bandit models, where the expected rewards are perturbed away from the linear subspace determined by the arms features. Although OFUL has recently been shown to be robust to r…
Pompeu Fabra University（庞培法布拉大学）；ICREA（加泰罗尼亚高级研究学院）；Barcelona Graduate School of Economics（巴塞罗那经济学研究生院）；Imperial College London（伦敦帝国理工学院）；Cisco Systems, Inc.（思科系统公司）
The fidelity bandits problem is a variant of the $K$-armed bandit problem in which the reward of each arm is augmented by a fidelity reward that provides the player with an additional payoff depending on how 'loyal' the player has been to that arm in the past. We propose two models for fidelity. In the loyalty-points model the amount of extra reward depends on the number of times the arm has previously been played. In the subscription model the additional reward depends on the current number of consecutive draws of the arm. We consider both stochastic and adversarial problems. Since single-arm…
Rice University（莱斯大学）；Institute for Advanced Study（高等研究院）；Princeton University（普林斯顿大学）
We present the first provable Least-Squares Value Iteration (LSVI) algorithms that have runtime complexity sublinear in the number of actions. We formulate the value function estimation procedure in value iteration as an approximate maximum inner product search problem and propose a locality sensitive hashing (LSH) [Indyk and Motwani STOC'98, Andoni and Razenshteyn STOC'15, Andoni, Laarhoven, Razenshteyn and Waingarten SODA'17] type data structure to solve this problem with sublinear time complexity. Moreover, we build the connections between the theory of approximate maximum inner product sea…
University of California, Berkeley（加州大学伯克利分校）；Princeton University（普林斯顿大学）；University of Washington（华盛顿大学）
We give novel algorithms for multi-task and lifelong linear bandits with shared representation. Specifically, we consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(\ll d)$ dimensional linear representation. For both the multi-task setting where we play the tasks concurrently, and the lifelong setting where we play tasks sequentially, we come up with novel algorithms that achieve $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T}\right)$ regret bounds, which matches the known minimax regret lower bound up to loga…
Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；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）；Grenoble INP（格勒诺布尔国立理工学院）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）；IBM Research（IBM研究院）；University of Pennsylvania（宾夕法尼亚大学）
We address the problem of \emph{`Internal Regret'} in \emph{Sleeping Bandits} in the fully adversarial setup, as well as draw connections between different existing notions of sleeping regrets in the multiarmed bandits (MAB) literature and consequently analyze the implications: Our first contribution is to propose the new notion of \emph{Internal Regret} for sleeping MAB. We then proposed an algorithm that yields sublinear regret in that measure, even for a completely adversarial sequence of losses and availabilities. We further show that a low sleeping internal regret always implies a low ext…
Sublinear Regret for a Class of Continuous-Time Linear-Quadratic Reinforcement Learning Problems
Department of Industrial Engineering and Operations Research, Columbia University（工业工程与运营管理系，哥伦比亚大学）；Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong（系统工程与工程管理系，香港中文大学）；Department of Industrial Engineering and Operations Research & Data Science Institute, Columbia University（工业工程与运营管理系及数据科学研究所，哥伦比亚大学）
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Microsoft Research（微软研究院）；Technion（以色列理工学院）
In this work, we consider the regret minimization problem for reinforcement learning in latent Markov Decision Processes (LMDP). In an LMDP, an MDP is randomly drawn from a set of $M$ possible MDPs at the beginning of the interaction, but the identity of the chosen MDP is not revealed to the agent. We first show that a general instance of LMDPs requires at least $Ω((SA)^M)$ episodes to even approximate the optimal policy. Then, we consider sufficient assumptions under which learning good policies requires polynomial number of episodes. We show that the key link is a notion of separation betwee…
Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins
School of Informatics, University of Edinburgh, Edinburgh, United Kingdom（爱丁堡大学信息学院）；School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom（爱丁堡大学数学学院）
University of California, Berkeley（加利福尼亚大学伯克利分校）；Purdue University（普渡大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）
In a Stackelberg game, a leader commits to a randomized strategy, and a follower chooses their best strategy in response. We consider an extension of a standard Stackelberg game, called a discrete-time dynamic Stackelberg game, that has an underlying state space that affects the leader's rewards and available strategies and evolves in a Markovian manner depending on both the leader and follower's selected strategies. Although standard Stackelberg games have been utilized to improve scheduling in security domains, their deployment is often limited by requiring complete information of the follow…
Institute of Science and Technology Austria（奥地利科学技术研究所）
We consider the problem of minimizing the regret in stochastic multi-armed bandit, when the measure of goodness of an arm is not the mean return, but some general function of the mean and the variance.We characterize the conditions under which learning is possible and present examples for which no natural algorithm can achieve sublinear regret.
We consider systems that require timely monitoring of sources over a communication network, where the cost of delayed information is unknown, time-varying and possibly adversarial. For the single source monitoring problem, we design algorithms that achieve sublinear regret compared to the best fixed policy in hindsight. For the multiple source scheduling problem, we design a new online learning algorithm called Follow-the-Perturbed-Whittle-Leader and show that it has low regret compared to the best fixed scheduling policy in hindsight, while remaining computationally feasible. The algorithm an…
Efficient Swap Regret Minimization in Combinatorial Bandits
National Technical University of Athens（雅典国立技术大学）；National and Kapodistrian University of Athens（雅典国立卡波季斯特里安大学）；Archimedes, Athena Research Center（雅典娜研究中心阿基米德部）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；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）；Grenoble INP（格勒诺布尔国立高等物理、数学与信息学院）；University of California, Irvine（加州大学尔湾分校）
CREST, ENSAE, Université Paris Saclay（巴黎萨克雷大学ENSAE-CREST）；Istituto Italiano di Tecnologia（意大利理工学院）；University College London（伦敦大学学院）
We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation used by the within-task algorithm, thereby transferring information from one task to the next. We show that when the within-task algorithm comes with some regret bound, our strategy inherits this good property. Our bounds are in expectation for a general loss function, and uniform for a convex loss. We discuss applications to dictionary learning and finite …
Microsoft Research（微软研究院）；Stanford University（斯坦福大学）
We consider the non-stochastic version of the (cooperative) multi-player multi-armed bandit problem. The model assumes no communication at all between the players, and furthermore when two (or more) players select the same action this results in a maximal loss. We prove the first $\sqrt{T}$-type regret guarantee for this problem, under the feedback model where collisions are announced to the colliding players. Such a bound was not known even for the simpler stochastic version. We also prove the first sublinear guarantee for the feedback model where collision information is not available, namel…
Carnegie Mellon University（卡内基梅隆大学）；INRIA Lille - Nord Europe（法国国家信息与自动化研究所里尔-北欧分部）
Learning from prior tasks and transferring that experience to improve future performance is critical for building lifelong learning agents. Although results in supervised and reinforcement learning show that transfer may significantly improve the learning performance, most of the literature on transfer is focused on batch learning tasks. In this paper we study the problem of \textit{sequential transfer in online learning}, notably in the multi-armed bandit framework, where the objective is to minimize the cumulative regret over a sequence of tasks by incrementally transferring knowledge from p…
Georgia Tech（佐治亚理工学院）；Microsoft Research Montreal（蒙特利尔微软研究院）
We present a reduction from reinforcement learning (RL) to no-regret online learning based on the saddle-point formulation of RL, by which "any" online algorithm with sublinear regret can generate policies with provable performance guarantees. This new perspective decouples the RL problem into two parts: regret minimization and function approximation. The first part admits a standard online-learning analysis, and the second part can be quantified independently of the learning algorithm. Therefore, the proposed reduction can be used as a tool to systematically design new RL algorithms. We demon…
Inria Lille（里尔法国国家信息与自动化研究所）；Facebook AI Research（脸书人工智能研究院）
We introduce and analyse two algorithms for exploration-exploitation in discrete and continuous Markov Decision Processes (MDPs) based on exploration bonuses. SCAL$^+$ is a variant of SCAL (Fruit et al., 2018) that performs efficient exploration-exploitation in any unknown weakly-communicating MDP for which an upper bound C on the span of the optimal bias function is known. For an MDP with $S$ states, $A$ actions and $Γ\leq S$ possible next states, we prove that SCAL$^+$ achieves the same theoretical guarantees as SCAL (i.e., a high probability regret bound of $\widetilde{O}(C\sqrt{ΓSAT})$), w…
