arXiv subjects

Simon S. Du

Publications and source records attributed to Simon S. Du.

At least 37 records · Page 2Linked to original sources

arXiv2025

The Crucial Role of Samplers in Online Direct Preference Optimization

Direct Preference Optimization (DPO) has emerged as a stable, scalable, and efficient solution for language model alignment. Despite its empirical success, the optimization properties, particularly the impact of samplers on its convergence rates, remain under-explored. In this paper, we provide a rigorous analysis of DPO's convergence rates with different sampling strategies under the exact gradient setting, revealing a surprising separation: uniform sampling achieves $\textbf{linear}$ convergence, while our proposed online sampler achieves $\textbf{quadratic}$ convergence. We further adapt the sampler to practical settings by incorporating posterior distributions and logit mixing, demonstrating improvements over previous methods. For example, it outperforms vanilla DPO by over $7.4$% on Safe-RLHF dataset. Our results not only offer insights into the theoretical understanding of DPO but also pave the way for further algorithm designs.

cs.LG↗

arXiv2025

Distributional Successor Features Enable Zero-Shot Policy Optimization

Intelligent agents must be generalists, capable of quickly adapting to various tasks. In reinforcement learning (RL), model-based RL learns a dynamics model of the world, in principle enabling transfer to arbitrary reward functions through planning. However, autoregressive model rollouts suffer from compounding error, making model-based RL ineffective for long-horizon problems. Successor features offer an alternative by modeling a policy's long-term state occupancy, reducing policy evaluation under new rewards to linear regression. Yet, zero-shot policy optimization for new tasks with successor features can be challenging. This work proposes a novel class of models, i.e., Distributional Successor Features for Zero-Shot Policy Optimization (DiSPOs), that learn a distribution of successor features of a stationary dataset's behavior policy, along with a policy that acts to realize different successor features achievable within the dataset. By directly modeling long-term outcomes in the dataset, DiSPOs avoid compounding error while enabling a simple scheme for zero-shot policy optimization across reward functions. We present a practical instantiation of DiSPOs using diffusion models and show their efficacy as a new class of transferable models, both theoretically and empirically across various simulated robotics problems. Videos and code available at https://weirdlabuw.github.io/dispo/.

cs.LG↗

arXiv2025

Learning Optimal Tax Design in Nonatomic Congestion Games

In multiplayer games, self-interested behavior among the players can harm the social welfare. Tax mechanisms are a common method to alleviate this issue and induce socially optimal behavior. In this work, we take the initial step of learning the optimal tax that can maximize social welfare with limited feedback in congestion games. We propose a new type of feedback named \emph{equilibrium feedback}, where the tax designer can only observe the Nash equilibrium after deploying a tax plan. Existing algorithms are not applicable due to the exponentially large tax function space, nonexistence of the gradient, and nonconvexity of the objective. To tackle these challenges, we design a computationally efficient algorithm that leverages several novel components: (1) a piece-wise linear tax to approximate the optimal tax; (2) extra linear terms to guarantee a strongly convex potential function; (3) an efficient subroutine to find the exploratory tax that can provide critical information about the game. The algorithm can find an $ε$-optimal tax with $O(βF^2/ε)$ sample complexity, where $β$ is the smoothness of the cost function and $F$ is the number of facilities.

cs.GT↗

arXiv2025

Preference-Based Multi-Agent Reinforcement Learning: Data Coverage and Algorithmic Techniques

We initiate the study of Preference-Based Multi-Agent Reinforcement Learning (PbMARL), exploring both theoretical foundations and empirical validations. We define the task as identifying the Nash equilibrium from a preference-only offline dataset in general-sum games, a problem marked by the challenge of sparse feedback signals. Our theory establishes the upper complexity bounds for Nash Equilibrium in effective PbMARL, demonstrating that single-policy coverage is inadequate and highlighting the importance of unilateral dataset coverage. These theoretical insights are verified through comprehensive experiments. To enhance the practical performance, we further introduce two algorithmic techniques. (1) We propose a Mean Squared Error (MSE) regularization along the time axis to achieve a more uniform reward distribution and improve reward learning outcomes. (2) We propose an additional penalty based on the distribution of the dataset to incorporate pessimism, improving stability and effectiveness during training. Our findings underscore the multifaceted approach required for PbMARL, paving the way for effective preference-based multi-agent systems.

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arXiv2024

Unleashing the Power of Pre-trained Language Models for Offline Reinforcement Learning

Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets. In real-world scenarios, data collection could be costly and risky; therefore, offline RL becomes particularly challenging when the in-domain data is limited. Given recent advances in Large Language Models (LLMs) and their few-shot learning prowess, this paper introduces $\textbf{La}$nguage Models for $\textbf{Mo}$tion Control ($\textbf{LaMo}$), a general framework based on Decision Transformers to effectively use pre-trained Language Models (LMs) for offline RL. Our framework highlights four crucial components: (1) Initializing Decision Transformers with sequentially pre-trained LMs, (2) employing the LoRA fine-tuning method, in contrast to full-weight fine-tuning, to combine the pre-trained knowledge from LMs and in-domain knowledge effectively, (3) using the non-linear MLP transformation instead of linear projections, to generate embeddings, and (4) integrating an auxiliary language prediction loss during fine-tuning to stabilize the LMs and retain their original abilities on languages. Empirical results indicate $\textbf{LaMo}$ achieves excellent performance in sparse-reward tasks and closes the gap between value-based offline RL methods and decision transformers in dense-reward tasks. In particular, our method demonstrates superior performance in scenarios with limited data samples.

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arXiv2024

Anytime Acceleration of Gradient Descent

This work investigates stepsize-based acceleration of gradient descent with {\em anytime} convergence guarantees. For smooth (non-strongly) convex optimization, we propose a stepsize schedule that allows gradient descent to achieve convergence guarantees of $O(T^{-1.119})$ for any stopping time $T$, where the stepsize schedule is predetermined without prior knowledge of the stopping time. This result provides an affirmative answer to a COLT open problem \citep{kornowski2024open} regarding whether stepsize-based acceleration can yield anytime convergence rates of $o(T^{-1})$. We further extend our theory to yield anytime convergence guarantees of $\exp(-Ω(T/κ^{0.893}))$ for smooth and strongly convex optimization, with $κ$ being the condition number.

cs.LG↗

arXiv2024

Learning to Cooperate with Humans using Generative Agents

Training agents that can coordinate zero-shot with humans is a key mission in multi-agent reinforcement learning (MARL). Current algorithms focus on training simulated human partner policies which are then used to train a Cooperator agent. The simulated human is produced either through behavior cloning over a dataset of human cooperation behavior, or by using MARL to create a population of simulated agents. However, these approaches often struggle to produce a Cooperator that can coordinate well with real humans, since the simulated humans fail to cover the diverse strategies and styles employed by people in the real world. We show \emph{learning a generative model of human partners} can effectively address this issue. Our model learns a latent variable representation of the human that can be regarded as encoding the human's unique strategy, intention, experience, or style. This generative model can be flexibly trained from any (human or neural policy) agent interaction data. By sampling from the latent space, we can use the generative model to produce different partners to train Cooperator agents. We evaluate our method -- \textbf{G}enerative \textbf{A}gent \textbf{M}odeling for \textbf{M}ulti-agent \textbf{A}daptation (GAMMA) -- on Overcooked, a challenging cooperative cooking game that has become a standard benchmark for zero-shot coordination. We conduct an evaluation with real human teammates, and the results show that GAMMA consistently improves performance, whether the generative model is trained on simulated populations or human datasets. Further, we propose a method for posterior sampling from the generative model that is biased towards the human data, enabling us to efficiently improve performance with only a small amount of expensive human interaction data.

cs.LG↗

arXiv2024

Decoding-Time Language Model Alignment with Multiple Objectives

Aligning language models (LMs) to human preferences has emerged as a critical pursuit, enabling these models to better serve diverse user needs. Existing methods primarily focus on optimizing LMs for a single reward function, limiting their adaptability to varied objectives. Here, we propose $\textbf{multi-objective decoding (MOD)}$, a decoding-time algorithm that outputs the next token from a linear combination of predictions of all base models, for any given weightings over different objectives. We exploit a common form among a family of $f$-divergence regularized alignment approaches (such as PPO, DPO, and their variants) to identify a closed-form solution by Legendre transform, and derive an efficient decoding strategy. Theoretically, we show why existing approaches can be sub-optimal even in natural settings and obtain optimality guarantees for our method. Empirical results demonstrate the effectiveness of the algorithm. For example, compared to a parameter-merging baseline, MOD achieves 12.8% overall reward improvement when equally optimizing towards $3$ objectives. Moreover, we experiment with MOD on combining three fully-finetuned LLMs of different model sizes, each aimed at different objectives such as safety, coding, and general user preference. Unlike traditional methods that require careful curation of a mixture of datasets to achieve comprehensive improvement, we can quickly experiment with preference weightings using MOD to find the best combination of models. Our best combination reduces toxicity on Toxigen to nearly 0% and achieves 7.9--33.3% improvement across other three metrics ($\textit{i.e.}$, Codex@1, GSM-COT, BBH-COT).

cs.LG↗

arXiv2024

Offline congestion games: How feedback type affects data coverage requirement

This paper investigates when one can efficiently recover an approximate Nash Equilibrium (NE) in offline congestion games. The existing dataset coverage assumption in offline general-sum games inevitably incurs a dependency on the number of actions, which can be exponentially large in congestion games. We consider three different types of feedback with decreasing revealed information. Starting from the facility-level (a.k.a., semi-bandit) feedback, we propose a novel one-unit deviation coverage condition and give a pessimism-type algorithm that can recover an approximate NE. For the agent-level (a.k.a., bandit) feedback setting, interestingly, we show the one-unit deviation coverage condition is not sufficient. On the other hand, we convert the game to multi-agent linear bandits and show that with a generalized data coverage assumption in offline linear bandits, we can efficiently recover the approximate NE. Lastly, we consider a novel type of feedback, the game-level feedback where only the total reward from all agents is revealed. Again, we show the coverage assumption for the agent-level feedback setting is insufficient in the game-level feedback setting, and with a stronger version of the data coverage assumption for linear bandits, we can recover an approximate NE. Together, our results constitute the first study of offline congestion games and imply formal separations between different types of feedback.

cs.GT↗

arXiv2024

An Experimental Design Framework for Label-Efficient Supervised Finetuning of Large Language Models

Supervised finetuning (SFT) on instruction datasets has played a crucial role in achieving the remarkable zero-shot generalization capabilities observed in modern large language models (LLMs). However, the annotation efforts required to produce high quality responses for instructions are becoming prohibitively expensive, especially as the number of tasks spanned by instruction datasets continues to increase. Active learning is effective in identifying useful subsets of samples to annotate from an unlabeled pool, but its high computational cost remains a barrier to its widespread applicability in the context of LLMs. To mitigate the annotation cost of SFT and circumvent the computational bottlenecks of active learning, we propose using experimental design. Experimental design techniques select the most informative samples to label, and typically maximize some notion of uncertainty and/or diversity. In our work, we implement a framework that evaluates several existing and novel experimental design techniques and find that these methods consistently yield significant gains in label efficiency with little computational overhead. On generative tasks, our methods achieve the same generalization performance with only $50\%$ of annotation cost required by random sampling.

cs.CL↗

arXiv2024

Understanding the Gains from Repeated Self-Distillation

Self-Distillation is a special type of knowledge distillation where the student model has the same architecture as the teacher model. Despite using the same architecture and the same training data, self-distillation has been empirically observed to improve performance, especially when applied repeatedly. For such a process, there is a fundamental question of interest: How much gain is possible by applying multiple steps of self-distillation? To investigate this relative gain, we propose studying the simple but canonical task of linear regression. Our analysis shows that the excess risk achieved by multi-step self-distillation can significantly improve upon a single step of self-distillation, reducing the excess risk by a factor as large as $d$, where $d$ is the input dimension. Empirical results on regression tasks from the UCI repository show a reduction in the learnt model's risk (MSE) by up to 47%.

cs.LG↗

arXiv2024

Refined Sample Complexity for Markov Games with Independent Linear Function Approximation

Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL). It was long believed that the "curse of multi-agents" (i.e., the algorithmic performance drops exponentially with the number of agents) is unavoidable until several recent works (Daskalakis et al., 2023; Cui et al., 2023; Wang et al., 2023). While these works resolved the curse of multi-agents, when the state spaces are prohibitively large and (linear) function approximations are deployed, they either had a slower convergence rate of $O(T^{-1/4})$ or brought a polynomial dependency on the number of actions $A_{\max}$ -- which is avoidable in single-agent cases even when the loss functions can arbitrarily vary with time. This paper first refines the AVLPR framework by Wang et al. (2023), with an insight of designing *data-dependent* (i.e., stochastic) pessimistic estimation of the sub-optimality gap, allowing a broader choice of plug-in algorithms. When specialized to MGs with independent linear function approximations, we propose novel *action-dependent bonuses* to cover occasionally extreme estimation errors. With the help of state-of-the-art techniques from the single-agent RL literature, we give the first algorithm that tackles the curse of multi-agents, attains the optimal $O(T^{-1/2})$ convergence rate, and avoids $\text{poly}(A_{\max})$ dependency simultaneously.

cs.LG↗

arXiv2024

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 approach 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 SFT and online RL, where a frozen reflection model (player) assists the policy model (player). 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 1.56B fine-tuned with Reflect-RL outperforms larger open-source LMs, such as Mistral 7B. The benchmarks, dataset, and code involved in this work are publicly available: https://github.com/zhourunlong/Reflect-RL.

cs.LG↗

arXiv2024

Rethinking Transformers in Solving POMDPs

Sequential decision-making algorithms such as reinforcement learning (RL) in real-world scenarios inevitably face environments with partial observability. This paper scrutinizes the effectiveness of a popular architecture, namely Transformers, in Partially Observable Markov Decision Processes (POMDPs) and reveals its theoretical limitations. We establish that regular languages, which Transformers struggle to model, are reducible to POMDPs. This poses a significant challenge for Transformers in learning POMDP-specific inductive biases, due to their lack of inherent recurrence found in other models like RNNs. This paper casts doubt on the prevalent belief in Transformers as sequence models for RL and proposes to introduce a point-wise recurrent structure. The Deep Linear Recurrent Unit (LRU) emerges as a well-suited alternative for Partially Observable RL, with empirical results highlighting the sub-optimal performance of the Transformer and considerable strength of LRU.

cs.LG↗

arXiv2024

A Black-box Approach for Non-stationary Multi-agent Reinforcement Learning

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve $\widetilde{O}\left(Δ^{1/4}T^{3/4}\right)$ regret when the degree of nonstationarity, as measured by total variation $Δ$, is known, and $\widetilde{O}\left(Δ^{1/5}T^{4/5}\right)$ regret when $Δ$ is unknown, where $T$ is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

cs.LG↗

arXiv2024

Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy. This paper studies the grokking phenomenon in theoretical setups and shows that it can be induced by a dichotomy of early and late phase implicit biases. Specifically, when training homogeneous neural nets with large initialization and small weight decay on both classification and regression tasks, we prove that the training process gets trapped at a solution corresponding to a kernel predictor for a long time, and then a very sharp transition to min-norm/max-margin predictors occurs, leading to a dramatic change in test accuracy.

cs.LG↗

arXiv2024

Horizon-Free Regret for Linear Markov Decision Processes

A recent line of works showed regret bounds in reinforcement learning (RL) can be (nearly) independent of planning horizon, a.k.a.~the horizon-free bounds. However, these regret bounds only apply to settings where a polynomial dependency on the size of transition model is allowed, such as tabular Markov Decision Process (MDP) and linear mixture MDP. We give the first horizon-free bound for the popular linear MDP setting where the size of the transition model can be exponentially large or even uncountable. In contrast to prior works which explicitly estimate the transition model and compute the inhomogeneous value functions at different time steps, we directly estimate the value functions and confidence sets. We obtain the horizon-free bound by: (1) maintaining multiple weighted least square estimators for the value functions; and (2) a structural lemma which shows the maximal total variation of the inhomogeneous value functions is bounded by a polynomial factor of the feature dimension.

cs.LG↗

arXiv2024

A Reduction-based Framework for Sequential Decision Making with Delayed Feedback

We study stochastic delayed feedback in general multi-agent sequential decision making, which includes bandits, single-agent Markov decision processes (MDPs), and Markov games (MGs). We propose a novel reduction-based framework, which turns any multi-batched algorithm for sequential decision making with instantaneous feedback into a sample-efficient algorithm that can handle stochastic delays in sequential decision making. By plugging different multi-batched algorithms into our framework, we provide several examples demonstrating that our framework not only matches or improves existing results for bandits, tabular MDPs, and tabular MGs, but also provides the first line of studies on delays in sequential decision making with function approximation. In summary, we provide a complete set of sharp results for multi-agent sequential decision making with delayed feedback.

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