In this paper, as a study of reinforcement learning, we converge the Q function to unbounded rewards such as Gaussian distribution. From the central limit theorem, in some real-world applications it is natural to assume that rewards follow a Gaussian distribution , but existing proofs cannot guarantee convergence of the Q-function. Furthermore, in the distribution-type reinforcement learning and Bayesian reinforcement learning that have become popular in recent years, it is better to allow the reward to have a Gaussian distribution. Therefore, in this paper, we prove the convergence of the Q-function under the condition of $E[r(s,a)^2]<\infty$, which is much more relaxed than the existing research. Finally, as a bonus, a proof of the policy gradient theorem for distributed reinforcement learning is also posted.
Inspired by the Reward-Biased Maximum Likelihood Estimate method of adaptive control, we propose RBMLE -- a novel family of learning algorithms for stochastic multi-armed bandits (SMABs). For a broad range of SMABs including both the parametric Exponential Family as well as the non-parametric sub-Gaussian/Exponential family, we show that RBMLE yields an index policy. To choose the bias-growth rate $α(t)$ in RBMLE, we reveal the nontrivial interplay between $α(t)$ and the regret bound that generally applies in both the Exponential Family as well as the sub-Gaussian/Exponential family bandits. T…
Generative adversarial imitation learning (GAIL) is a popular inverse reinforcement learning approach for jointly optimizing policy and reward from expert trajectories. A primary question about GAIL is whether applying a certain policy gradient algorithm to GAIL attains a global minimizer (i.e., yields the expert policy), for which existing understanding is very limited. Such global convergence has been shown only for the linear (or linear-type) MDP and linear (or linearizable) reward. In this paper, we study GAIL under general MDP and for nonlinear reward function classes (as long as the obje…
We show two average-reward off-policy control algorithms, Differential Q-learning (Wan, Naik, & Sutton 2021a) and RVI Q-learning (Abounadi Bertsekas & Borkar 2001), converge in weakly communicating MDPs. Weakly communicating MDPs are the most general MDPs that can be solved by a learning algorithm with a single stream of experience. The original convergence proofs of the two algorithms require that the solution set of the average-reward optimality equation only has one degree of freedom, which is not necessarily true for weakly communicating MDPs. To the best of our knowledge, our results are …
Non-asymptotic Convergence of Average-reward Q-learning with Options
Indian Institute of Science（印度科学学院）；Universitat Pompeu Fabra（庞培法布拉大学）；Univ. Lille, Inria, CNRS- CRIStAL, Centrale Lille（里尔大学、Inria、法国国家科学研究中心CRIStAL实验室、里尔中央理工学院）
Evolution strategy (ES) has been shown great promise in many challenging reinforcement learning (RL) tasks, rivaling other state-of-the-art deep RL methods. Yet, there are two limitations in the current ES practice that may hinder its otherwise further capabilities. First, most current methods rely on Monte Carlo type gradient estimators to suggest search direction, where the policy parameter is, in general, randomly sampled. Due to the low accuracy of such estimators, the RL training may suffer from slow convergence and require more iterations to reach optimal solution. Secondly, the landscap…
Tencent Jarvis Lab（腾讯Jarvis实验室）；RALI & Mila, Université de Montréal（蒙特利尔大学RALI实验室与Mila研究所）；Sun Yat-sen University（中山大学）
For task-oriented dialog systems, training a Reinforcement Learning (RL) based Dialog Management module suffers from low sample efficiency and slow convergence speed due to the sparse rewards in RL.To solve this problem, many strategies have been proposed to give proper rewards when training RL, but their rewards lack interpretability and cannot accurately estimate the distribution of state-action pairs in real dialogs. In this paper, we propose a multi-level reward modeling approach that factorizes a reward into a three-level hierarchy: domain, act, and slot. Based on inverse adversarial rein…
Fluid human-agent communication is essential for the future of human-in-the-loop reinforcement learning. An agent must respond appropriately to feedback from its human trainer even before they have significant experience working together. Therefore, it is important that learning agents respond well to various feedback schemes human trainers are likely to provide. This work analyzes the COnvergent Actor-Critic by Humans (COACH) algorithm under three different types of feedback-policy feedback, reward feedback, and advantage feedback. For these three feedback types, we find that COACH can behave…
We develop an exactly solvable framework of Markov decision process with a finite horizon, and continuous state and action spaces. We first review the exact solution of conventional linear quadratic regulation with a linear transition and a Gaussian noise, whose optimal policy does not depend on the Gaussian noise, which is an undesired feature in the presence of significant noises. It motivates us to investigate exact solutions which depend on noise. To do so, we generalize the reward accumulation to be a general binary commutative and associative operation. By a new multiplicative accumulati…
Reinforcement learning algorithms typically assume rewards to be sampled from light-tailed distributions, such as Gaussian or bounded. However, a wide variety of real-world systems generate rewards that follow heavy-tailed distributions. We consider such scenarios in the setting of undiscounted reinforcement learning. By constructing a lower bound, we show that the difficulty of learning heavy-tailed rewards asymptotically dominates the difficulty of learning transition probabilities. Leveraging techniques from robust mean estimation, we propose Heavy-UCRL2 and Heavy-Q-Learning, and show that …
University of Colorado Boulder（科罗拉多大学博尔德分校）；University of Central Florida（中佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）
The success of reinforcement learning in typical settings is predicated on Markovian assumptions on the reward signal by which an agent learns optimal policies. In recent years, the use of reward machines has relaxed this assumption by enabling a structured representation of non-Markovian rewards. In particular, such representations can be used to augment the state space of the underlying decision process, thereby facilitating non-Markovian reinforcement learning. However, these reward machines cannot capture the semantics of stochastic reward signals. In this paper, we make progress on this f…
University of Texas（德克萨斯大学）；University of California（加利福尼亚大学）
We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks. We establish the convergence rates of the maximum likelihood estimation (MLE) for these models. Our proof technique is based on a novel notion of \emph{algebraic independence} of the expert functions. Drawing on optimal transport theory, we establish a connection between the algebraic independence and a certain class of partial differential equations (PDEs). Exploiting this connection allows us to derive convergence rates and minimax lower bounds for parameter estimation.
Global Convergence of Average Reward Constrained MDPs with Neural Critic and General Policy Parameterization
Department of Computer Science University of Maryland College Park（计算机科学系大学马里兰大学学院公园）；Indian Institute of Technology, Kanpur（印度理工学院坎浦尔）；Department of Electrical Engineering Indian Institute of Technology, Kanpur（电气工程系印度理工学院坎浦尔）；Department of Industrial Engineering Purdue University West Lafayette（工业工程系普渡大学威斯康星拉法叶）
We propose a generic reward shaping approach for improving the rate of convergence in reinforcement learning (RL), called Self Improvement Based REwards, or SIBRE. The approach is designed for use in conjunction with any existing RL algorithm, and consists of rewarding improvement over the agent's own past performance. We prove that SIBRE converges in expectation under the same conditions as the original RL algorithm. The reshaped rewards help discriminate between policies when the original rewards are weakly discriminated or sparse. Experiments on several well-known benchmark environments wit…
The ability to compute an accurate reward function is essential for optimising a dialogue policy via reinforcement learning. In real-world applications, using explicit user feedback as the reward signal is often unreliable and costly to collect. This problem can be mitigated if the user's intent is known in advance or data is available to pre-train a task success predictor off-line. In practice neither of these apply for most real world applications. Here we propose an on-line learning framework whereby the dialogue policy is jointly trained alongside the reward model via active learning with …
Technion Israel Institute of Technology（以色列理工学院）；DeepMind（深度思维）
Solving tasks in Reinforcement Learning is no easy feat. As the goal of the agent is to maximize the accumulated reward, it often learns to exploit loopholes and misspecifications in the reward signal resulting in unwanted behavior. While constraints may solve this issue, there is no closed form solution for general constraints. In this work we present a novel multi-timescale approach for constrained policy optimization, called `Reward Constrained Policy Optimization' (RCPO), which uses an alternative penalty signal to guide the policy towards a constraint satisfying one. We prove the converge…
Department of Computer Science University of New Hampshire（计算机科学系新罕布什尔大学）；Department of Computing & Mathematical Sciences California Institute of Technology（计算与数学科学系加州理工学院）；Tencent AI Lab（腾讯AI实验室）
Huazhong University of Science and Technology（华中科技大学）；South East University（东南大学）；Central Queensland University（中央昆士兰大学）
(This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.) To improve the efficiency of deep reinforcement learning (DRL)-based methods for robot manipulator trajectory planning in random working environments, we present three dense reward functions. These rewards differ from the traditional sparse reward. First, a posture reward function is proposed to speed up the learning process with a more reasonable trajectory by modeling the distance and direction constraints, which can reduce th…
University of Alberta（阿尔伯塔大学）；Amii（阿尔伯塔机器智能研究所）；DeepMind
We extend the options framework for temporal abstraction in reinforcement learning from discounted Markov decision processes (MDPs) to average-reward MDPs. Our contributions include general convergent off-policy inter-option learning algorithms, intra-option algorithms for learning values and models, as well as sample-based planning variants of our learning algorithms. Our algorithms and convergence proofs extend those recently developed by Wan, Naik, and Sutton. We also extend the notion of option-interrupting behavior from the discounted to the average-reward formulation. We show the efficac…
