Exploration-Exploitation

Reinforcement Learning from Human Feedback (RLHF) has shown great potential in fine-tuning Large Language Models (LLMs) to align with human preferences. Existing methods perform preference alignment from a fixed dataset, which can be limited in data coverage and the resulting reward model is hard to generalize in out-of-distribution responses. Thus, online RLHF is more desirable to empower the LLM to explore outside the support of the initial dataset by iteratively collecting the prompt-response pairs. In this paper, we study the fundamental problem in online RLHF, i.e., how to explore for LLM. We give a theoretical motivation in linear reward assumption to show that an optimistic reward with an upper confidence bound (UCB) term leads to a provably efficient RLHF policy. Then, we reformulate our objective to direct preference optimization with an exploration term, where the UCB-term can be converted to a count-based exploration bonus. We further propose a practical algorithm, named Count-based Online Preference Optimization (COPO), which leverages a simple coin-flip counting module to estimate the pseudo-count of a prompt-response pair in previously collected data. COPO encourages LLMs to balance exploration and preference optimization in an iterative manner, which enlarges the exploration space and the entire data coverage of iterative LLM policies. We conduct online RLHF experiments on Zephyr and Llama-3 models. The results on instruction-following and standard academic benchmarks show that COPO significantly increases performance.

We investigate the problem of batched best arm identification in multi-armed bandits, where we want to find the best arm from a set of $n$ arms while minimizing both the number of samples and batches. We introduce an algorithm that achieves near-optimal sample complexity and features an instance-sensitive batch complexity, which breaks the $\log(1/\Delta_2)$ barrier. The main contribution of our algorithm is a novel sample allocation scheme that effectively balances exploration and exploitation for batch sizes. Experimental results indicate that our approach is more batch-efficient across various setups. We also extend this framework to the problem of batched best arm identification in linear bandits and achieve similar improvements.

How to balance between exploration and exploitation in an uncertain environment is a central challenge in reinforcement learning. In contrast, humans and animals have demonstrated superior exploration efficiency in novel environments. To understand how the brain’s neural network controls exploration under uncertainty, we analyzed the dynamical systems model of a biological neural network that controls explore-exploit decisions during foraging. Mathematically, this model (named the Brain Bandit Net, or BBN) is a special type of stochastic continuous Hopfield network. We show through theory and simulation that BBN can perform posterior sampling of action values with a tunable bias towards or against uncertain options. We then demonstrate that, in multi-armed bandit (MAB) tasks, BBN can generate probabilistic choice behavior with a flexible uncertainty bias resembling human and animal choice patterns. In addition to its high efficiency in MAB tasks, BBN can also be embedded with reinforcement learning algorithms to accelerate learning in MDP tasks. Altogether, our findings reveal the theoretical foundation for efficient exploration in biological neural networks and propose a general, brain-inspired algorithm for enhancing exploration in RL.

Reward shaping is a reinforcement learning technique that addresses the sparse-reward problem by providing frequent, informative feedback. We propose an efficient self-adaptive reward-shaping mechanism that uses success rates derived from historical experiences as shaped rewards. The success rates are sampled from Beta distributions, which evolve from uncertainty to reliability as data accumulates. Initially, shaped rewards are stochastic to encourage exploration, gradually becoming more certain to promote exploitation and maintain a natural balance between exploration and exploitation. We apply Kernel Density Estimation (KDE) with Random Fourier Features (RFF) to derive Beta distributions, providing a computationally efficient solution for continuous and high-dimensional state spaces. Our method, validated on tasks with extremely sparse rewards, improves sample efficiency and convergence stability over relevant baselines.

Tool learning enables Large Language Models (LLMs) to interact with external environments by invoking tools, serving as an effective strategy to mitigate the limitations inherent in their pre-training data. In this process, tool documentation plays a crucial role by providing usage instructions for LLMs, thereby facilitating effective tool utilization. This paper concentrates on the critical challenge of bridging the comprehension gap between LLMs and external tools due to the inadequacies and inaccuracies inherent in existing human-centric tool documentation. We propose a novel framework, DRAFT, aimed at Dynamically Refining tool documentation through the Analysis of Feedback and Trials emanating from LLMs' interactions with external tools. This methodology pivots on an innovative trial-and-error approach, consisting of three distinct learning phases: experience gathering, learning from experience, and documentation rewriting, to iteratively enhance the tool documentation. This process is further optimized by implementing a diversity-promoting exploration strategy to ensure explorative diversity and a tool-adaptive termination mechanism to prevent overfitting while enhancing efficiency. Extensive experiments on multiple datasets demonstrate that DRAFT's iterative, feedback-based refinement significantly ameliorates documentation quality, fostering a deeper comprehension and more effective utilization of tools by LLMs. Notably, our analysis reveals that the tool documentation refined via our approach demonstrates robust cross-model generalization capabilities.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. Recently, the approach to self-improvement has shifted toward a more dynamic, online fashion through iterative training processes. However, the critical factors underlying the mechanism of these self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to explore and generate high-quality responses among multiple candidates (exploration); and (2) the reliability of external rewards in selecting the best responses from the generated outputs (exploitation). These factors are inherently moving targets throughout the self-improvement cycles, yet their dynamics are rarely discussed in prior research -- It remains unclear what impedes continual model enhancement after only a few iterations. Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well due to shifts in distribution from the original policy. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-teaching effectiveness based on the current policy model and available rewards. Our experiments in mathematical reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance. Crucially, this work deconstructs the opaque nature of self-training algorithms, elucidating the interpretable dynamics throughout the process and highlighting current limitations for future research to address.

Imitation learning is a central problem in reinforcement learning where the goal is to learn a policy that mimics the expert's behavior. In practice, it is often challenging to learn the expert policy from a limited number of demonstrations accurately due to the complexity of the state space. Moreover, it is essential to explore the environment and collect data to achieve beyond-expert performance. To overcome these challenges, we propose a novel imitation learning algorithm called Imitation Learning with Double Exploration (ILDE), which implements exploration in two aspects: (1) optimistic policy optimization via an exploration bonus that rewards state-action pairs with high uncertainty to potentially improve the convergence to the expert policy, and (2) curiosity-driven exploration of the states that deviate from the demonstration trajectories to potentially yield beyond-expert performance. Empirically, we demonstrate that ILDE outperforms the state-of-the-art imitation learning algorithms in terms of sample efficiency and achieves beyond-expert performance on Atari and MuJoCo tasks with fewer demonstrations than in previous work. We also provide a theoretical justification of ILDE as an uncertainty-regularized policy optimization method with optimistic exploration, leading to a regret growing sublinearly in the number of episodes.

A rich line of recent works studies how participants in matching markets learn their unknown preferences through iterative interactions with each other. The two sides of participants in the market can be respectively formulated as players and arms in the bandit problem. To ensure market stability, the objective is to minimize the stable regret of each player. Though existing works provide significant theoretical upper bounds for players' stable regret, the results heavily rely on the assumption that each participant has a strict preference ranking. However, in real applications, multiple candidates (e.g., workers in the labor market and students in school admission) usually demonstrate comparable performance levels, making it challenging for participants (e.g., employers and schools) to differentiate and rank their preferences. To deal with the potential indifferent preferences, we propose an adaptive exploration algorithm based on arm-guided Gale-Shapley (AE-AGS). We show that its stable regret is of order $O(NK \log T / \Delta^2)$, where $N$ is the number of players, $K$ the number of arms, $T$ the total time horizon, and $\Delta$ the minimum non-zero preference gap. Extensive experiments demonstrate the algorithm's effectiveness in handling such complex situations and its consistent superiority over baselines.

Despite their power, Transformers face challenges with long sequences due to the quadratic complexity of self-attention. To address this limitation, methods like $k$-Nearest-Neighbor ($k$NN) attention have been introduced [Roy et al., 2017], enabling each token to attend to only its $k$ closest tokens. While $k$NN attention has shown empirical success in making Transformers more efficient, its exact approximation guarantees have not been theoretically analyzed. In this work, we establish a theoretical framework for $k$NN attention, reformulating self-attention as expectations over softmax distributions and leveraging lazy Gumbel sampling [Mussmann et al., 2017] with $k$NN indices for efficient approximation. Building on this framework, we also propose novel sub-quadratic algorithms that approximate self-attention gradients by leveraging efficient sampling techniques, such as Markov Chain-based estimation. Finally, we demonstrate the practical effectiveness of these algorithms through empirical experiments, showcasing their benefits in both training and inference.

The contextual multi-armed bandit (MAB) problem is crucial in sequential decision-making. A line of research, known as online clustering of bandits, extends contextual MAB by grouping similar users into clusters, utilizing shared features to improve learning efficiency. However, existing algorithms, which rely on the upper confidence bound (UCB) strategy, struggle to gather adequate statistical information to accurately identify unknown user clusters. As a result, their theoretical analyses require several strong assumptions about the "diversity" of contexts generated by the environment, leading to impractical settings, complicated analyses, and poor practical performance. Removing these assumptions has been a long-standing open problem in the clustering of bandits literature. In this work, we provide two partial solutions. First, we introduce an additional exploration phase to accelerate the identification of clusters. We integrate this general strategy into both graph-based and set-based algorithms and propose two new algorithms, UniCLUB and UniSCLUB. Remarkably, our algorithms require substantially weaker assumptions and simpler theoretical analyses while achieving superior cumulative regret compared to previous studies. Second, inspired by the smoothed analysis framework, we propose a more practical setting that eliminates the requirement for i.i.d. context generation used in previous studies, thus enhancing the performance of existing algorithms for online clustering of bandits. Extensive evaluations on both synthetic and real-world datasets demonstrate that our proposed algorithms outperform existing approaches.