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Reinforcement Learning

Vivienne Wang, Tinghuai Wang, wenyan yang, Joni-kristian Kamarainen, Joni Pajarinen

In goal-conditioned hierarchical reinforcement learning (HRL), a high-level policy specifies a subgoal for the low-level policy to reach. Effective HRL hinges on a suitable subgoal representation function, abstracting state space into latent subgoal space and inducing varied low-level behaviors. Existing methods adopt a subgoal representation that provides a deterministic mapping from state space to latent subgoal space. Instead, this paper utilizes Gaussian Processes (GPs) for the first probabilistic subgoal representation. Our method employs a GP prior on the latent subgoal space to learn a posterior distribution over the subgoal representation functions while exploiting the long-range correlation in the state space through learnable kernels. This enables an adaptive memory that integrates long-range subgoal information from prior planning steps allowing to cope with stochastic uncertainties. Furthermore, we propose a novel learning objective to facilitate the simultaneous learning of probabilistic subgoal representations and policies within a unified framework. In experiments, our approach outperforms state-of-the-art baselines in standard benchmarks but also in environments with stochastic elements and under diverse reward conditions. Additionally, our model shows promising capabilities in transferring low-level policies across different tasks.

Applications · Robotics

Yufei Wang, Zhou Xian, Feng Chen, Johnson Tsun-Hsuan Wang, Yian Wang, Katerina Fragkiadaki, Zackory Erickson, David Held, Chuang Gan

We present RoboGen, a generative robotic agent that automatically learns diverse robotic skills at scale via generative simulation. RoboGen leverages the latest advancements in foundation and generative models. Instead of directly adapting these models to produce policies or low-level actions, we advocate for a generative scheme, which uses these models to automatically generate diversified tasks, scenes, and training supervisions, thereby scaling up robotic skill learning with minimal human supervision. Our approach equips a robotic agent with a self-guided propose-generate-learn cycle: the agent first proposes interesting tasks and skills to develop, and then generates simulation environments by populating pertinent assets with proper spatial configurations. Afterwards, the agent decomposes the proposed task into sub-tasks, selects the optimal learning approach (reinforcement learning, motion planning, or trajectory optimization), generates required training supervision, and then learns policies to acquire the proposed skill. Our fully generative pipeline can be queried repeatedly, producing an endless stream of skill demonstrations associated with diverse tasks and environments.

Reinforcement Learning · Planning

Paul Mattes, Rainer Schlosser, Ralf Herbrich

One of the biggest challenges to modern deep reinforcement learning (DRL) algorithms is sample efficiency. Many approaches learn a world model in order to train an agent entirely in imagination, eliminating the need for direct environment interaction during training. However, these methods often suffer from either a lack of imagination accuracy, exploration capabilities, or runtime efficiency. We propose HIEROS, a hierarchical policy that learns time abstracted world representations and imagines trajectories at multiple time scales in latent space. HIEROS uses an S5 layer-based world model, which predicts next world states in parallel during training and iteratively during environment interaction. Due to the special properties of S5 layers, our method can train in parallel and predict next world states iteratively during imagination. This allows for more efficient training than RNN-based world models and more efficient imagination than Transformer-based world models. We show that our approach outperforms the state of the art in terms of mean and median normalized human score on the Atari 100k benchmark, and that our proposed world model is able to predict complex dynamics very accurately. We also show that HIEROS displays superior exploration capabilities compared to existing approaches.

Reinforcement Learning · Multi-agent

Yannik Mahlau, Frederik Schubert, Bodo Rosenhahn

The combination of self-play and planning has achieved great successes in sequential games, for instance in Chess and Go. However, adapting algorithms such as AlphaZero to simultaneous games poses a new challenge. In these games, missing information about concurrent actions of other agents is a limiting factor as they may select different Nash equilibria or do not play optimally at all. Thus, it is vital to model the behavior of the other agents when interacting with them in simultaneous games. To this end, we propose Albatross: AlphaZero for Learning Bounded-rational Agents and Temperature-based Response Optimization using Simulated Self-play. Albatross learns to play the novel equilibrium concept of a Smooth Best Response Logit Equilibrium (SBRLE), which enables cooperation and competition with agents of any playing strength. We perform an extensive evaluation of Albatross on a set of cooperative and competitive simultaneous perfect-information games. In contrast to AlphaZero, Albatross is able to exploit weak agents in the competitive game of Battlesnake. Additionally, it yields an improvement of 37.6% compared to previous state of the art in the cooperative Overcooked benchmark.

Theory · Reinforcement Learning and Planning

Jianliang He, Siyu Chen, Fengzhuo Zhang, Zhuoran Yang

In this work, from a theoretical lens, we aim to understand why large language model (LLM) empowered agents are able to solve decision-making problems in the physical world. To this end, consider a hierarchical reinforcement learning (RL) model where the LLM Planner and the Actor perform high-level task planning and low-level execution, respectively. Under this model, the LLM Planner navigates a partially observable Markov decision process (POMDP) by iteratively generating language-based subgoals via prompting. Under proper assumptions on the pretraining data, we prove that the pretrained LLM Planner effectively performs Bayesian aggregated imitation learning (BAIL) through in-context learning. Additionally, we highlight the necessity for exploration beyond the subgoals derived from BAIL by proving that naively executing the subgoals returned by LLM leads to a linear regret. As a remedy, we introduce an $\epsilon$-greedy exploration strategy to BAIL, which is proven to incur sublinear regret when the pretraining error is small. Finally, we extend our theoretical framework to include scenarios where the LLM Planner serves as a world model for inferring the transition model of the environment and to multi-agent settings, enabling coordination among multiple Actors.

Theory · Reinforcement Learning and Planning

Andi Nika, Debmalya Mandal, Parameswaran Kamalaruban, Georgios Tzannetos, Goran Radanovic, Adish Singla

In this paper, we take a step towards a deeper understanding of learning from human preferences by systematically comparing the paradigm of reinforcement learning from human feedback (RLHF) with the recently proposed paradigm of direct preference optimization (DPO). We focus our attention on the class of loglinear policy parametrization and linear reward functions. In order to compare the two paradigms, we first derive minimax statistical bounds on the suboptimality gap induced by both RLHF and DPO, assuming access to an oracle that exactly solves the optimization problems. We provide a detailed discussion on the relative comparison between the two paradigms, simultaneously taking into account the sample size, policy and reward class dimensions, and the regularization temperature. Moreover, we extend our analysis to the approximate optimization setting and derive exponentially decaying convergence rates for both RLHF and DPO. Next, we analyze the setting where the ground-truth reward is not realizable and find that, while RLHF incurs a constant additional error, DPO retains its asymptotically decaying gap by just tuning the temperature accordingly. Finally, we extend our comparison to the Markov decision process setting, where we generalize our results with exact optimization. To the best of our knowledge, we are the first to provide such a comparative analysis for RLHF and DPO.

Theory · Reinforcement Learning and Planning

Tianchen Zhou, Hairi, Haibo Yang, Jia (Kevin) Liu, Tian Tong, Fan Yang, Michinari Momma, Yan Gao

Reinforcement learning with multiple, potentially conflicting objectives is pervasive in real-world applications, while this problem remains theoretically under-explored. This paper tackles the multi-objective reinforcement learning (MORL) problem and introduces an innovative actor-critic algorithm named MOAC which finds a policy by iteratively making trade-offs among conflicting reward signals. Notably, we provide the first analysis of finite-time Pareto-stationary convergence and corresponding sample complexity in both discounted and average reward settings. Our approach has two salient features: (a) MOAC mitigates the cumulative estimation bias resulting from finding an optimal common gradient descent direction out of stochastic samples. This enables provable convergence rate and sample complexity guarantees independent of the number of objectives; (b) With proper momentum coefficient, MOAC initializes the weights of individual policy gradients using samples from the environment, instead of manual initialization. This enhances the practicality and robustness of our algorithm. Finally, experiments conducted on a real-world dataset validate the effectiveness of our proposed method.

Optimization · Learning for Optimization

zhi Zheng, Shunyu Yao, Zhenkun Wang, Tong Xialiang, Mingxuan Yuan, Ke Tang

The min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have exhibited advantages in solving efficiency and optimality. However, these methods fail to exploit the problem-specific properties in learning representations, resulting in less effective features for decoding optimal routes. This paper considers the sequential planning process of min-max VRPs as two coupled optimization tasks: customer partition for different routes and customer navigation in each route (i.e., partition and navigation). To effectively process min-max VRP instances, we present a novel attention-based Partition-and-Navigation encoder (P&N Encoder) that learns distinct embeddings for partition and navigation. Furthermore, we utilize an inherent symmetry in decoding routes and develop an effective agent-permutation-symmetric (APS) loss function. Experimental results demonstrate that the proposed Decoupling-Partition-Navigation (DPN) method significantly surpasses existing learning-based methods in both single-depot and multi-depot min-max VRPs. Our code is available at

Theory · Reinforcement Learning and Planning

Weiye Zhao, Feihan Li, Yifan Sun, Rui Chen, Tianhao Wei, Changliu Liu

In recent years, trust region on-policy reinforcement learning has achieved impressive results in addressing complex control tasks and gaming scenarios. However, contemporary state-of-the-art algorithms within this category primarily emphasize improvement in expected performance, lacking the ability to control over the worst-case performance outcomes. To address this limitation, we introduce a novel objective function, optimizing which leads to guaranteed monotonic improvement in the lower probability bound of performance with high confidence. Building upon this groundbreaking theoretical advancement, we further introduce a practical solution called Absolute Policy Optimization (APO). Our experiments demonstrate the effectiveness of our approach across challenging continuous control benchmark tasks and extend its applicability to mastering Atari games. Our findings reveal that APO as well as its efficient variation Proximal Absolute Policy Optimization (PAPO) significantly outperforms state-of-the-art policy gradient algorithms, resulting in substantial improvements in worst-case performance, as well as expected performance.

Theory · Reinforcement Learning and Planning

Kaiwen Wang, Owen Oertell, Alekh Agarwal, Nathan Kallus, Wen Sun

In this paper, we prove that Distributional Reinforcement Learning (DistRL), which learns the return distribution, can obtain second-order bounds in both online and offline RL in general settings with function approximation. Second-order bounds are instance-dependent bounds that scale with the variance of return, which we prove are tighter than the previously known small-loss bounds of distributional RL. To the best of our knowledge, our results are the first second-order bounds for low-rank MDPs and for offline RL. When specializing to contextual bandits (one-step RL problem), we show that a distributional learning based optimism algorithm achieves a second-order worst-case regret bound, and a second-order gap dependent bound, simultaneously. We also empirically demonstrate the benefit of DistRL in contextual bandits on real-world datasets. We highlight that our analysis with DistRL is relatively simple, follows the general framework of optimism in the face of uncertainty and does not require weighted regression. Our results suggest that DistRL is a promising framework for obtaining second-order bounds in general RL settings, thus further reinforcing the benefits of DistRL.

Theory · Reinforcement Learning and Planning

Shuai Zhang, Heshan Fernando, Miao Liu, Keerthiram Murugesan, Songtao Lu, Pin-Yu Chen, Tianyi Chen, Meng Wang

This paper studies the transfer reinforcement learning (RL) problem where multiple RL problems have different reward functions but share the same underlying transition dynamics. In this setting, the Q-function of each RL problem (task) can be decomposed into a successor feature (SF) and a reward mapping: the former characterizes the transition dynamics, and the latter characterizes the task-specific reward function. This Q-function decomposition, coupled with a policy improvement operator known as generalized policy improvement (GPI), reduces the sample complexity of finding the optimal Q-function, and thus the SF & GPI framework exhibits promising empirical performance compared to traditional RL methods like Q-learning. However, its theoretical foundations remain largely unestablished, especially when learning the successor features using deep neural networks (SF-DQN). This paper studies the provable knowledge transfer using SFs-DQN in transfer RL problems. We establish the first convergence analysis with provable generalization guarantees for SF-DQN with GPI. The theory reveals that SF-DQN with GPI outperforms conventional RL approaches, such as deep Q-network, in terms of both faster convergence rate and better generalization. Numerical experiments on real and synthetic RL tasks support the superior performance of SF-DQN & GPI, aligning with our theoretical findings.

Theory · Reinforcement Learning and Planning

Tonghe Zhang, Yu Chen, Longbo Huang

This work pioneers regret analysis of risk-sensitive reinforcement learning in partially observable environments with hindsight observation, addressing a gap in theoretical exploration. We introduce a novel formulation that integrates hindsight observations into a Partially Observable Markov Decision Process (POMDP) framework, where the goal is to optimize accumulated reward under the entropic risk measure. We develop the first provably efficient RL algorithm tailored for this setting. We also prove by rigorous analysis that our algorithm achieves polynomial regret $\tilde{O}\left(\frac{e^{|{\gamma}|H}-1}{|{\gamma}|H}H^2\sqrt{KHS^2OA}\right)$, which outperforms or matches existing upper bounds when the model degenerates to risk-neutral or fully observable settings. We adopt the method of change-of-measure and develop a novel analytical tool of beta vectors to streamline mathematical derivations. These techniques are of particular interest to the theoretical study of reinforcement learning.

Reinforcement Learning · Planning

Yuhui Wang, Weida Li, Francesco Faccio, Qingyuan Wu, Jürgen Schmidhuber

Value iteration networks (VINs) enable end-to-end learning for planning tasks by employing a differentiable "planning module" that approximates the value iteration algorithm. However, long-term planning remains a challenge because training very deep VINs is difficult. To address this problem, we embed highway value iteration---a recent algorithm designed to facilitate long-term credit assignment---into the structure of VINs. This improvement augments the "planning module" of the VIN with three additional components: 1) an "aggregate gate," which constructs skip connections to improve information flow across many layers; 2) an "exploration module," crafted to increase the diversity of information and gradient flow in spatial dimensions; 3) a "filter gate" designed to ensure safe exploration. The resulting novel highway VIN can be trained effectively with hundreds of layers using standard backpropagation. In long-term planning tasks requiring hundreds of planning steps, deep highway VINs outperform both traditional VINs and several advanced, very deep NNs.

Reinforcement Learning · Function Approximation

Sattar Vakili, Farhang Nabiei, Da-shan Shiu, Alberto Bernacchia

Achieving sample efficiency in Reinforcement Learning (RL) is primarily hinged on the efficient exploration of the underlying environment, but it is still unknown what are the best exploration strategies in different settings. We consider the *reward-free* RL problem, which operates in two phases: an exploration phase, where the agent gathers exploration trajectories over episodes irrespective of any predetermined reward function, and a subsequent planning phase, where a reward function is introduced. The agent then utilizes the episodes from the exploration phase to calculate a near-optimal policy. Existing algorithms and sample complexities for reward-free RL are limited to tabular, linear or very smooth function approximations, leaving the problem largely open for more general cases. We consider a broad range of kernel-based function approximations, including non-smooth kernels, and propose an algorithm based on adaptive domain partitioning. We show that our algorithm achieves order-optimal sample complexity for a large class of common kernels, which includes Matérn and Neural Tangent kernels.

Theory · Reinforcement Learning and Planning

Danil Provodin, Maurits Kaptein, Mykola Pechenizkiy

We present a new algorithm based on posterior sampling for learning in Constrained Markov Decision Processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous empirically compared to the existing algorithms. Our main theoretical result is a Bayesian regret bound for each cost component of $\tilde{O} (DS\sqrt{AT})$ for any communicating CMDP with $S$ states, $A$ actions, and diameter $D$. This regret bound matches the lower bound in order of time horizon $T$ and is the best-known regret bound for communicating CMDPs achieved by a computationally tractable algorithm. Empirical results show that our posterior sampling algorithm outperforms the existing algorithms for constrained reinforcement learning.

Reinforcement Learning

Xinyi Ni, Guanlin Liu, Lifeng Lai

Exploration is a crucial phase in reinforcement learning (RL). The reward-free RL paradigm, as explored by (Jin et al., 2020), offers an efficient method to design exploration algorithms for risk-neutral RL across various reward functions with a single exploration phase. However, as RL applications in safety critical settings grow, there's an increasing need for risk-sensitive RL, which considers potential risks in decision-making. Yet, efficient exploration strategies for risk-sensitive RL remain underdeveloped. This study presents a novel risk-sensitive reward-free framework based on Conditional Value-at-Risk (CVaR), designed to effectively address CVaR RL for any given reward function through a single exploration phase. We introduce the CVaR-RF-UCRL algorithm, which is shown to be $(\epsilon,p)$-PAC, with a sample complexity upper bounded by $\tilde{\mathcal{O}}\left(\frac{S^2AH^4}{\epsilon^2\tau^2}\right)$ with $\tau$ being the risk tolerance parameter. We also prove a $\Omega\left(\frac{S^2AH^2}{\epsilon^2\tau}\right)$ lower bound for any CVaR-RF exploration algorithm, demonstrating the near-optimality of our algorithm. Additionally, we propose the planning algorithms: CVaR-VI and its more practical variant, CVaR-VI-DISC. The effectiveness and practicality of our CVaR reward-free approach are further validated through numerical experiments.

Reinforcement Learning · Batch/Offline

Jeremy McMahan, Giovanni Artiglio, Qiaomin Xie

We study robust Markov games (RMG) with $s$-rectangular uncertainty. We show a general equivalence between computing a robust Nash equilibrium (RNE) of a $s$-rectangular RMG and computing a Nash equilibrium (NE) of an appropriately constructed regularized MG. The equivalence result yields a planning algorithm for solving $s$-rectangular RMGs, as well as provable robustness guarantees for policies computed using regularized methods. However, we show that even for just reward-uncertain two-player zero-sum matrix games, computing an RNE is PPAD-hard. Consequently, we derive a special uncertainty structure called efficient player-decomposability and show that RNE for two-player zero-sum RMG in this class can be provably solved in polynomial time. This class includes commonly used uncertainty sets such as $L_1$ and $L_\infty$ ball uncertainty sets.

Theory · Reinforcement Learning and Planning

Davide Maran, Alberto Maria Metelli, Matteo Papini, Marcello Restelli

Obtaining no-regret guarantees for reinforcement learning (RL) in the case of problems with continuous state and/or action spaces is still one of the major open challenges in the field. Recently, a variety of solutions have been proposed, but besides very specific settings, the general problem remains unsolved. In this paper, we introduce a novel structural assumption on the Markov decision processes (MDPs), namely $\nu-$smoothness, that generalizes most of the settings proposed so far (e.g., linear MDPs and Lipschitz MDPs). To face this challenging scenario, we propose two algorithms for regret minimization in $\nu-$smooth MDPs. Both algorithms build upon the idea of constructing an MDP representation through an orthogonal feature map based on Legendre polynomials. The first algorithm, Legendre-Eleanor, archives the no-regret property under weaker assumptions but is computationally inefficient, whereas the second one, Legendre-LSVI, runs in polynomial time, although for a smaller class of problems. After analyzing their regret properties, we compare our results with state-of-the-art ones from RL theory, showing that our algorithms achieve the best guarantees.

Theory · Reinforcement Learning and Planning

Orin Levy, Asaf Cassel, Alon Cohen, Yishay Mansour

We present the E-UC$^3$RL algorithm for regret minimization in Stochastic Contextual Markov Decision Processes (CMDPs). The algorithm operates under the minimal assumptions of realizable function class and access to *offline* least squares and log loss regression oracles. Our algorithm is efficient (assuming efficient offline regression oracles) and enjoys a regret guarantee of $ \widetilde{O}(H^3 \sqrt{T |S| |A|d_{\mathrm{E}}(\mathcal{P}) \log (|\mathcal{F}| |\mathcal{P}|/ \delta) )}) $ , with $T$ being the number of episodes, $S$ the state space, $A$ the action space, $H$ the horizon, $\mathcal{P}$ and $\mathcal{F}$ are finite function classes used to approximate the context-dependent dynamics and rewards, respectively, and $d_{\mathrm{E}}(\mathcal{P})$ is the Eluder dimension of $\mathcal{P}$ w.r.t the Hellinger distance. To the best of our knowledge, our algorithm is the first efficient and rate-optimal regret minimization algorithm for CMDPs that operates under the general offline function approximation setting. In addition, we extend the Eluder dimension to general bounded metrics which may be of independent interest.

Theory · Reinforcement Learning and Planning

Kevin Leahy, Makai Mann, Zachary Serlin

Compositionality is a critical aspect of scalable system design. Here, we focus on Boolean composition of learned tasks as opposed to functional or sequential composition. Existing Boolean composition for Reinforcement Learning focuses on reaching a satisfying absorbing state in environments with discrete action spaces, but does not support composable safety (i.e., avoidance) constraints. We provide three contributions: i) introduce two distinct notions of compositional safety semantics; ii) show how to enforce either safety semantics, prove correctness, and analyze the trade-offs between the two safety notions; and iii) extend Boolean composition from discrete action spaces to continuous action spaces. We demonstrate these techniques using modified versions of value iteration in a grid world, Deep Q-Network (DQN) in a grid world with image observations, and Twin Delayed DDPG (TD3) in a continuous-observation and continuous-action Bullet physics environment