Reflect-RL: Two-Player Online RL Fine-Tuning for LMs

As language models (LMs) demonstrate their capabilities in various fields, their application to tasks requiring multi-round interactions has become increasingly popular. These tasks usually have complex dynamics, so supervised fine-tuning (SFT) on a limited offline dataset does not yield good performance. However, only a few works attempted to directly train the LMs within interactive decision-making environments. We aim to create an effective mechanism to fine-tune LMs with online reinforcement learning (RL) in these environments. We propose Reflect-RL, a two-player system to fine-tune an LM using online RL, where a frozen reflection model assists the policy model. To generate data for the warm-up SFT stage, we use negative example generation to enhance the error-correction ability of the reflection model. Furthermore, we designed single-prompt action enumeration and applied curriculum learning to allow the policy model to learn more efficiently. Empirically, we verify that Reflect-RL outperforms SFT and online RL without reflection. Testing results indicate GPT-2-xl after Reflect-RL also outperforms those of untuned pre-trained LMs, such as Mistral 7B.

Free from Bellman Completeness: Trajectory Stitching via Model-based Return-conditioned Supervised Learning

Off-policy dynamic programming (DP) techniques such as $Q$-learning have proven to be an important technique for solving sequential decision-making problems. However, in the presence of function approximation such algorithms are not guaranteed to converge, often diverging due to the absence of Bellman-completeness in the function classes considered, a crucial condition for the success of DP-based methods. In this paper, we show how off-policy learning techniques based on return-conditioned supervised learning (RCSL) are able to circumvent these challenges of Bellman completeness, converging under significantly more relaxed assumptions inherited from supervised learning. We prove there exists a natural environment in which if one uses two-layer multilayer perceptron as the function approximator, the layer width needs to grow linearly with the state space size to satisfy Bellman-completeness while a constant layer width is enough for RCSL. These findings take a step towards explaining the superior empirical performance of RCSL methods compared to DP-based methods in environments with near-optimal datasets. Furthermore, in order to learn from sub-optimal datasets, we propose a simple framework called MBRCSL, granting RCSL methods the ability of dynamic programming to stitch together segments from distinct trajectories. MBRCSL leverages learned dynamics models and forward sampling to accomplish trajectory stitching while avoiding the need for Bellman completeness that plagues all dynamic programming algorithms. We propose both theoretical analysis and experimental evaluation to back these claims, outperforming state-of-the-art model-free and model-based offline RL algorithms across several simulated robotics problems.

Sharp Variance-Dependent Bounds in Reinforcement Learning: Best of Both Worlds in Stochastic and Deterministic Environments

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a) and use new analysis techniques show to this algorithm enjoys variance-dependent bounds with respect to our proposed norms. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Understanding Curriculum Learning in Policy Optimization for Solving Combinatorial Optimization Problems

Over the recent years, reinforcement learning (RL) has shown impressive performance in finding strategic solutions for game environments, and recently starts to show promising results in solving combinatorial optimization (CO) problems, inparticular when coupled with curriculum learning to facilitate training. Despite emerging empirical evidence, theoretical study on why RL helps is still at its early stage. This paper presents the first systematic study on policy optimization methods for solving CO problems. We show that CO problems can be naturally formulated as latent Markov Decision Processes (LMDPs), and prove convergence bounds on natural policy gradient (NPG) for solving LMDPs. Furthermore, our theory explains the benefit of curriculum learning: it can find a strong sampling policy and reduce the distribution shift, a critical quantity that governs the convergence rate in our theorem. For a canonical combinatorial problem, Secretary Problem, we formally prove that distribution shift is reduced exponentially with curriculum learning. Our theory also shows we can simplify the curriculum learning scheme used in prior work from multi-step to single-step. Lastly, we provide extensive experiments on Secretary Problem and Online Knapsack to empirically verify our findings.

Stochastic Shortest Path: Minimax, Parameter-Free and Towards Horizon-Free Regret

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.