Exploration-Exploitation

Unsupervised pretraining has been transformative in many supervised domains. However, applying such ideas to reinforcement learning (RL) presents a unique challenge in that fine-tuning does not involve mimicking task-specific data, but rather exploring and locating the solution through iterative self-improvement. In this work, we study how unlabeled offline trajectory data can be leveraged to learn efficient exploration strategies. While prior data can be used to pretrain a set of low-level skills, or as additional off-policy data for online RL, it has been unclear how to combine these ideas effectively for online exploration. Our method SUPE (Skills from Unlabeled Prior data for Exploration) demonstrates that a careful combination of these ideas compounds their benefits. Our method first extracts low-level skills using a variational autoencoder (VAE), and then pseudo-labels unlabeled trajectories with optimistic rewards and high-level action labels, transforming prior data into high-level, task-relevant examples that encourage novelty-seeking behavior. Finally, SUPE uses these transformed examples as additional off-policy data for online RL to learn a high-level policy that composes pretrained low-level skills to explore efficiently. In our experiments, SUPE consistently outperforms prior strategies across a suite of 42 long-horizon, sparse-reward tasks.

Motivated by an open direction in existing literature, we study the 1-identification problem, a fundamental multi-armed bandit formulation on pure exploration. The goal is to determine whether there exists an arm whose mean reward is at least a known threshold $\mu_0$, or to output \textsf{None} if it believes such an arm does not exist. The agent needs to guarantee its output is correct with probability at least $1-\delta$. Degenne & Koolen 2019 has established the asymptotically tight sample complexity for the 1-identification problem, but they commented that the non-asymptotic analysis remains unclear. We design a new algorithm Sequential-Exploration-Exploitation (SEE), and conduct theoretical analysis from the non-asymptotic perspective. Novel to the literature, we achieve near optimality, in the sense of matching upper and lower bounds on the pulling complexity. The gap between the upper and lower bounds is up to a polynomial logarithmic factor. The numerical result also indicates the effectiveness of our algorithm, compared to existing benchmarks.

The exploration \& exploitation dilemma poses significant challenges in reinforcement learning (RL). Recently, curiosity-based exploration methods achieved great success in tackling hard-exploration problems. However, they necessitate extensive hyperparameter tuning on different environments, which heavily limits the applicability and accessibility of this line of methods. In this paper, we characterize this problem via analysis of the agent behavior, concluding the fundamental difficulty of choosing a proper hyperparameter. We then identify the difficulty and the instability of the optimization when the agent learns with curiosity. We propose our method, hyperparameter robust exploration (\textbf{Hyper}), which extensively mitigates the problem by effectively regularizing the visitation of the exploration and decoupling the exploitation to ensure stable training. We theoretically justify that \textbf{Hyper} is provably efficient under function approximation setting and empirically demonstrate its appealing performance and robustness in various environments.

In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations. We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task. We then give a general batched algorithm and prove upper bounds on its expected sample complexity and batch complexity. We illustrate both lower and upper bounds on best-arm identification and thresholding bandits.

This paper studies a pure exploration problem with linear bandit feedback on continuous arm sets, aiming to identify an $\epsilon$-optimal arm with high probability. Previous approaches for continuous arm sets have employed instance-independent methods due to technical challenges such as the infinite dimensionality of the space of probability measures and the non-smoothness of the objective function. This paper proposes a novel, tractable algorithm that addresses these challenges by leveraging a reparametrization of the sampling distribution and projected subgradient descent. However, this approach introduces new challenges related to the projection and reconstruction of the distribution from the reparametrization. We address these by focusing on the connection to the approximate Carath\'eodory problem. Compared to the original optimization problem on the infinite-dimensional space, our method is tractable, requiring only the solution of quadratic and fractional quadratic problems on the arm set. We establish an instance-dependent optimality for our method, and empirical results on synthetic data demonstrate its superiority over existing instance-independent baselines.

Optimizing objective functions subject to constraints is fundamental in many real-world applications. However, these constraints are often not readily defined and must be inferred from expert agent behaviors, a problem known as Inverse Constraint Inference. Inverse Constrained Reinforcement Learning (ICRL) is a common solver for recovering feasible constraints in complex environments, relying on training samples collected from interactive environments. However, the efficacy and efficiency of current sampling strategies remain unclear. We propose a strategic exploration framework for sampling with guaranteed efficiency to bridge this gap. By defining the feasible cost set for ICRL problems, we analyze how estimation errors in transition dynamics and the expert policy influence the feasibility of inferred constraints. Based on this analysis, we introduce two exploratory algorithms to achieve efficient constraint inference via 1) dynamically reducing the bounded aggregate error of cost estimations or 2) strategically constraining the exploration policy around plausibly optimal ones. Both algorithms are theoretically grounded with tractable sample complexity, and their performance is validated empirically across various environments.

Despite their success in many domains, large language models (LLMs) remain under-studied in scenarios requiring optimal decision-making under uncertainty. This is crucial as many real-world applications, ranging from personalized recommendations to healthcare interventions, demand that LLMs not only predict but also actively learn to make optimal decisions through exploration. In this work, we measure LLMs' (in)ability to make optimal decisions in bandits, a state-less reinforcement learning setting relevant to many applications. We develop a comprehensive suite of environments, including both context-free and contextual bandits with varying task difficulties, to benchmark LLMs' performance. Motivated by the existence of optimal exploration algorithms, we propose efficient ways to integrate this algorithmic knowledge into LLMs: by providing explicit algorithm-guided support during inference; and through algorithm distillation via in-context demonstrations and fine-tuning, using synthetic data generated from these algorithms. Impressively, these techniques allow us to achieve superior exploration performance with smaller models, surpassing larger models on various tasks. We conducted an extensive ablation study to shed light on various factors, such as task difficulty and data representation, that influence the efficiency of LLM exploration. Additionally, we conduct a rigorous analysis of the LLM's exploration efficiency using the concept of regret, linking its ability to explore to the model size and underlying algorithm.

Existing reward shaping techniques for sparse-reward reinforcement learning generally fall into two categories: novelty-based exploration bonuses and significance-based hidden state values. The former promotes exploration but can lead to distraction from task objectives, while the latter facilitates stable convergence but often lacks sufficient early exploration. To address these limitations, we propose Dual Random Networks Distillation (DuRND), a novel reward shaping framework that efficiently balances exploration and exploitation in a unified mechanism. DuRND leverages two lightweight random network modules to simultaneously compute two complementary rewards: a novelty reward to encourage directed exploration and a contribution reward to assess progress toward task completion. With low computational overhead, DuRND excels in high-dimensional environments with challenging sparse rewards, such as Atari, VizDoom, and MiniWorld, outperforming several benchmarks.

Soft Actor-Critic (SAC) has achieved notable success in continuous control tasks but struggles in sparse reward settings, where infrequent rewards make efficient exploration challenging. While novelty-based exploration methods address this issue by encouraging the agent to explore novel states, they are not trivial to apply to SAC. In particular, managing the interaction between novelty-based exploration and SAC’s stochastic policy can lead to inefficient exploration and redundant sample collection. In this paper, we propose KEA (Keeping Exploration Alive) which tackles the inefficiencies in balancing exploration strategies when combining SAC with novelty-based exploration. KEA integrates a novelty-augmented SAC with a standard SAC agent, proactively coordinated via a switching mechanism. This coordination allows the agent to maintain stochasticity in high-novelty regions, enhancing exploration efficiency and reducing repeated sample collection. We first analyze this potential issue in a 2D navigation task, and then evaluate KEA on the DeepSea hard-exploration benchmark as well as sparse reward control tasks from the DeepMind Control Suite. Compared to state-of-the-art novelty-based exploration baselines, our experiments show that KEA significantly improves learning efficiency and robustness in sparse reward setups.

Control tasks with safety requirements under high levels of model uncertainty are increasingly common. Machine learning techniques are frequently used to address such tasks, typically by leveraging model error bounds to specify robust constraint-based safety filters. However, if the learned model uncertainty is very high, the corresponding filters are potentially invalid, meaning no control input satisfies the constraints imposed by the safety filter. While most works address this issue by assuming some form of safe backup controller, ours tackles it by collecting additional data on the fly using a Gaussian process bandit-type algorithm. We combine a control barrier function with a learned model to specify a robust certificate that ensures safety if feasible. Whenever infeasibility occurs, we leverage the control barrier function to guide exploration, ensuring the collected data contributes toward the closed-loop system safety. By combining a safety filter with exploration in this manner, our method provably achieves safety in a general setting that does not require any prior model or backup controller, provided that the true system lies in a reproducing kernel Hilbert space. To the best of our knowledge, it is the first safe learning-based control method that achieves this.

We study the linear bandit problem under limited adaptivity, known as the batched linear bandit. While existing approaches can achieve near-optimal regret in theory, they are often computationally prohibitive or underperform in practice. We propose BLAE, a novel batched algorithm that integrates arm elimination with regularized G-optimal design, achieving the minimax optimal regret (up to logarithmic factors in $T$) in both large-$K$ and small-$K$ regimes for the first time, while using only $O(\log\log T)$ batches. Our analysis introduces new techniques for batch-wise optimal design and refined concentration bounds. Crucially, BLAE demonstrates low computational overhead and strong empirical performance, outperforming state-of-the-art methods in extensive numerical evaluations. Thus, BLAE is the first algorithm to combine provable minimax-optimality in all regimes and practical superiority in batched linear bandits.

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of $\mathcal{O}(T^{-1/8})$ on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performances, with the best attainable rate being $\mathcal{O}(T^{-1/4})$ in contrast to the usual $\mathcal{O}(T^{-1/2})$ rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate. The first algorithm leverages a straightforward tradeoff between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.

Piecewise constant functions describe a variety of real-world phenomena in domains ranging from chemistry to manufacturing. In practice, it is often required to confidently identify the locations of the abrupt changes in these functions as quickly as possible. For this, we introduce a fixed-confidence piecewise constant bandit problem. Here, we sequentially query points in the domain and receive noisy evaluations of the function under bandit feedback. We provide instance-dependent lower bounds for the complexity of change point identification in this problem. These lower bounds illustrate that an optimal method should focus its sampling efforts adjacent to each of the change points, and the number of samples around each change point should be inversely proportional to the magnitude of the change. Building on this, we devise a simple and computationally efficient variant of Track-and-Stop and prove that it is asymptotically optimal in many regimes. We support our theoretical findings with experimental results in synthetic environments demonstrating the efficiency of our method.

A tenet of reinforcement learning is that the agent always observes rewards. However, this is not true in many realistic settings, e.g., a human observer may not always be available to provide rewards, sensors may be limited or malfunctioning, or rewards may be inaccessible during deployment. Monitored Markov decision processes (Mon-MDPs) have recently been proposed to model such settings. However, existing Mon-MDP algorithms have several limitations: they do not fully exploit the problem structure, cannot leverage a known monitor, lack worst-case guarantees for "unsolvable" Mon-MDPs without specific initialization, and offer only asymptotic convergence proofs. This paper makes three contributions. First, we introduce a model-based algorithm for Mon-MDPs that addresses these shortcomings. The algorithm employs two instances of model-based interval estimation: one to ensure that observable rewards are reliably captured, and another to learn the minimax-optimal policy. Second, we empirically demonstrate the advantages. We show faster convergence than prior algorithms in more than four dozen benchmarks, and even more dramatic improvements when the monitoring process is known. Third, we present the first finite-sample bound on performance. We show convergence to a minimax-optimal policy even when some rewards are never observable.

We investigate learning approximate Nash equilibrium (NE) policy profiles in two-player zero-sum imperfect information extensive-form games (IIEFGs) with last-iterate convergence guarantees. Existing algorithms either rely on full-information feedback or provide only asymptotic convergence rates. In contrast, we focus on the bandit feedback setting, where players receive feedback solely from the rewards associated with the experienced information set and action pairs in each episode. Our proposed algorithm employs a negentropy regularizer weighted by a "virtual transition" over the information set-action space to facilitate an efficient approximate policy update. Through a carefully designed virtual transition and leveraging the entropy regularization technique, we demonstrate finite-time last-iterate convergence to the NE with a rate of $\widetilde{\mathcal{O}}(k^{-\frac{1}{8}})$ under bandit feedback in each episode $k$. Empirical evaluations across various IIEFG instances show its competitive performance compared to baseline methods.

Many real-world bandit applications are characterized by sparse rewards, which can significantly hinder learning efficiency. Leveraging problem-specific structures for careful distribution modeling is recognized as essential for improving estimation efficiency in statistics. However, this approach remains under-explored in the context of bandits. To address this gap, we initiate the study of zero-inflated bandits, where the reward is modeled using a classic semi-parametric distribution known as the zero-inflated distribution. We develop algorithms based on the Upper Confidence Bound and Thompson Sampling frameworks for this specific structure. The superior empirical performance of these methods is demonstrated through extensive numerical studies.

The best arm identification problem requires identifying the best alternative (i.e., arm) in active experimentation using the smallest number of experiments (i.e., arm pulls), which is crucial for cost-efficient and timely decision-making processes. In the fixed confidence setting, an algorithm must stop data-dependently and return the estimated best arm with a correctness guarantee. Since this stopping time is random, we desire its distribution to have light tails. Unfortunately, many existing studies focus on high probability or in expectation bounds on the stopping time, which allow heavy tails and, for high probability bounds, even not stopping at all. We first prove that this never-stopping event can indeed happen for some popular algorithms. Motivated by this, we propose algorithms that provably enjoy an exponential-tailed stopping time, which improves upon the polynomial tail bound reported by Kalyanakrishnan et al. (2012). The first algorithm is based on a fixed budget algorithm called Sequential Halving along with a doubling trick. The second algorithm is a meta algorithm that takes in any fixed confidence algorithm with a high probability stopping guarantee and turns it into one that enjoys an exponential-tailed stopping time. Our results imply that there is much more to be desired for contemporary fixed confidence algorithms.

We study the problem of clustering a set of items based on bandit feedback. Each of the $n$ items is characterized by a feature vector, with a possibly large dimension $d$. The items are partitioned into two unknown groups, such that items within the same group share the same feature vector. We consider a sequential and adaptive setting in which, at each round, the learner selects one item and one feature, then observes a noisy evaluation of the item's feature. The learner's objective is to recover the correct partition of the items, while keeping the number of observations as small as possible. We provide an algorithm which relies on finding a relevant feature for the clustering task, leveraging the Sequential Halving algorithm. With probability at least $1-\delta$, we obtain an accurate recovery of the partition and derive an upper bound on the required budget . Furthermore, we derive an instance-dependent lower bound, which is tight in some relevant cases.

Parallel data collection has redefined Reinforcement Learning (RL), unlocking unprecedented efficiency and powering breakthroughs in large-scale real-world applications. In this paradigm, $N$ identical agents operate in $N$ replicas of an environment simulator, accelerating data collection by a factor of $N$. A critical question arises: *Does specializing the policies of the parallel agents hold the key to surpass the $N$ factor acceleration?* In this paper, we introduce a novel learning framework that maximizes the entropy of collected data in a parallel setting. Our approach carefully balances the entropy of individual agents with inter-agent diversity, effectively minimizing redundancies. The latter idea is implemented with a centralized policy gradient method, which shows promise when evaluated empirically against systems of identical agents, as well as synergy with batch RL techniques that can exploit data diversity. Finally, we provide an original concentration analysis that shows faster rates for specialized parallel sampling distributions, which supports our methodology and may be of independent interest.

This work investigates the problem of best arm identification for multi-agent multi-armed bandits. We consider $N$ agents grouped into $M$ clusters, where each cluster solves a stochastic bandit problem. The mapping between agents and bandits is \textit{a priori} unknown. Each bandit is associated with $K$ arms, and the goal is to identify the best arm for each agent under a $\delta$-probably correct ($\delta$-PC) framework, while minimizing sample complexity and communication overhead. We propose two novel algorithms: \emph{Clustering then Best Arm Identification} (\texttt{Cl-BAI}) and \emph{Best Arm Identification then Clustering} (\texttt{BAI-Cl}). \texttt{Cl-BAI} employs a two-phase approach that first clusters agents based on the bandit problems they are learning, followed by identifying the best arm for each cluster. \texttt{BAI-Cl} reverses the sequence by identifying the best arms first and then clustering agents accordingly. Both algorithms exploit the successive elimination framework to ensure computational efficiency and high accuracy. Theoretical analysis establishes $\delta$-PC guarantees for both methods, derives bounds on their sample complexity, and provides a lower bound for the problem class. Moreover, when $M$ is small (a constant), we show that the sample complexity of (a variant of) \texttt{BAI-Cl} is (order-wise) minimax optimal. Experiments on synthetic and real-world (Movie Lens, Yelp) data demonstrates the superior performance of the proposed algorithms in terms of sample and communication efficiency, particularly in settings where $M \ll N$.