NeurIPS 2024 Papers

We study the performance guarantees of exploration-free greedy algorithms for the linear contextual bandit problem. We introduce a novel condition, named the \textit{Local Anti-Concentration} (LAC) condition, which enables a greedy bandit algorithm to achieve provable efficiency. We show that the LAC condition is satisfied by a broad class of distributions, including Gaussian, exponential, uniform, Cauchy, and Student's~$t$ distributions, along with other exponential family distributions and their truncated variants. This significantly expands the class of distributions under which greedy algorithms can perform efficiently. Under our proposed LAC condition, we prove that the cumulative expected regret of the greedy algorithm for the linear contextual bandit is bounded by $\mathcal{O}(\operatorname{poly} \log T)$. Our results establish the widest range of distributions known to date that allow a sublinear regret bound for greedy algorithms, further achieving a sharp poly-logarithmic regret.

We provide a new understanding of the stochastic gradient bandit algorithm by showing that it converges to a globally optimal policy almost surely using \emph{any} constant learning rate. This result demonstrates that the stochastic gradient algorithm continues to balance exploration and exploitation appropriately even in scenarios where standard smoothness and noise control assumptions break down. The proofs are based on novel findings about action sampling rates and the relationship between cumulative progress and noise, and extend the current understanding of how simple stochastic gradient methods behave in bandit settings.

The ability to perform different skills can encourage agents to explore. In this work, we aim to construct a set of diverse skills that uniformly cover the state space. We propose a formalization of this search for diverse skills, building on a previous definition based on the mutual information between states and skills. We consider the distribution of states reached by a policy conditioned on each skill and leverage the successor state representation to maximize the difference between these skill distributions. We call this approach LEADS: Learning Diverse Skills through Successor State Representations. We demonstrate our approach on a set of maze navigation and robotic control tasks which show that our method is capable of constructing a diverse set of skills which exhaustively cover the state space without relying on reward or exploration bonuses. Our findings demonstrate that this new formalization promotes more robust and efficient exploration by combining mutual information maximization and exploration bonuses.

Iteratively improving and repairing source code with large language models (LLMs), known as refinement, has emerged as a popular way of generating programs that would be too complex to construct in one shot. Given a bank of test cases, together with a candidate program, an LLM can improve that program by being prompted with failed test cases. But it remains an open question how to best iteratively refine code, with prior work employing simple greedy or breadth-first strategies. We show here that refinement exposes an explore-exploit tradeoff: exploit by refining the program that passes the most test cases, or explore by refining a lesser considered program. We frame this as an arm-acquiring bandit problem, which we solve with Thompson Sampling. The resulting LLM-based program synthesis algorithm is broadly applicable: Across loop invariant synthesis, visual reasoning puzzles, and competition programming problems, we find that our new method can solve more problems using fewer language model calls.

Exploration in reinforcement learning (RL) remains an open challenge. RL algorithms rely on observing rewards to train the agent, and if informative rewards are sparse the agent learns slowly or may not learn at all. To improve exploration and reward discovery, popular algorithms rely on optimism. But what if sometimes rewards are unobservable, e.g., situations of partial monitoring in bandits and the recent formalism of monitored Markov decision process? In this case, optimism can lead to suboptimal behavior that does not explore further to collapse uncertainty. With this paper, we present a novel exploration strategy that overcomes the limitations of existing methods and guarantees convergence to an optimal policy even when rewards are not always observable. We further propose a collection of tabular environments for benchmarking exploration in RL (with and without unobservable rewards) and show that our method outperforms existing ones.

Choice models are essential for understanding decision-making processes in domains like online advertising, product recommendations, and assortment optimization. The Multinomial Logit (MNL) model is particularly versatile in selecting products or advertisements for display. However, challenges arise with unknown MNL parameters and delayed feedback, requiring sellers to learn customers’ choice behavior and make dynamic decisions with biased knowledge due to delays. We address these challenges by developing an algorithm that handles delayed feedback, balancing exploration and exploitation using confidence bounds and optimism. We first consider a censored setting where a threshold for considering feedback is imposed by business requirements. Our algorithm demonstrates a $\tilde{O}(\sqrt{NT})$ regret, with a matching lower bound up to a logarithmic term. Furthermore, we extend our analysis to environments with non-thresholded delays, achieving a $\tilde{O}(\sqrt{NT})$ regret. To validate our approach, we conduct experiments that confirm the effectiveness of our algorithm.

We propose a novel stochastic bandit algorithm that employs reward estimates using a tree ensemble model. Specifically, our focus is on a soft tree model, a variant of the conventional decision tree that has undergone both practical and theoretical scrutiny in recent years. By deriving several non-trivial properties of soft trees, we extend the existing analytical techniques used for neural bandit algorithms to our soft tree-based algorithm. We demonstrate that our algorithm achieves a smaller cumulative regret compared to the existing ReLU-based neural bandit algorithms. We also show that this advantage comes with a trade-off: the hypothesis space of the soft tree ensemble model is more constrained than that of a ReLU-based neural network.

In online Inverse Reinforcement Learning (IRL), the learner can collect samples about the dynamics of the environment to improve its estimate of the reward function. Since IRL suffers from identifiability issues, many theoretical works on online IRL focus on estimating the entire set of rewards that explain the demonstrations, named the *feasible reward set*. However, none of the algorithms available in literature can scale to problems with large state spaces. In this paper, we focus on the online IRL problem in Linear Markov Decision Processes (MDPs). We show that the structure offered by Linear MDPs is not sufficient for efficiently estimating the feasible set when the state space is large. As a consequence, we introduce the novel framework of *rewards compatibility*, which generalizes the notion of feasible set, and we develop CATY-IRL, a sample efficient algorithm whose complexity is independent of the size of the state space in Linear MDPs. When restricted to the tabular setting, we demonstrate that CATY-IRL is minimax optimal up to logarithmic factors. As a by-product, we show that Reward-Free Exploration (RFE) enjoys the same worst-case rate, improving over the state-of-the-art lower bound. Finally, we devise a unifying framework for IRL and RFE that may be of independent interest.

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose **N**on**e**pisodic **O**ptistmic **RL** (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of $\mathcal{O}(\beta_T \sqrt{T \Gamma_T})$ for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

We study a general clustering setting in which we have $n$ elements to be clustered, and we aim to perform as few queries as possible to an oracle that returns a noisy sample of the weighted similarity between two elements. Our setting encompasses many application domains in which the similarity function is costly to compute and inherently noisy. We introduce two novel formulations of online learning problems rooted in the paradigm of Pure Exploration in Combinatorial Multi-Armed Bandits (PE-CMAB): fixed confidence and fixed budget settings. For both settings, we design algorithms that combine a sampling strategy with a classic approximation algorithm for correlation clustering and study their theoretical guarantees. Our results are the first examples of polynomial-time algorithms that work for the case of PE-CMAB in which the underlying offline optimization problem is NP-hard.

Prod is a seminal algorithm in full-information online learning, which has been conjectured to be fundamentally sub-optimal for multi-armed bandits. By leveraging the interpretation of Prod as a first-order OMD approximation, we present the following surprising results: 1. Variants of Prod can obtain optimal regret for adversarial multi-armed bandits. 2. There exists a simple and (arguably) importance-weighting free variant with optimal rate. 3. One can even achieve best-both-worlds guarantees with logarithmic regret in the stochastic regime. The bandit algorithms in this work use simple arithmetic update rules without the need of solving optimization problems typical in prior work. Finally, the results directly improve the state of the art of incentive-compatible bandits.

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated probabilities are embedded in the posterior distribution. However, when confronted with data of high dimensionality (such as images), visualizing this distribution becomes a formidable challenge, necessitating the application of effective summarization techniques before user examination. In this work, we introduce a new approach for visualizing posteriors across multiple levels of granularity using *tree*-valued predictions. Our method predicts a tree-valued hierarchical summarization of the posterior distribution for any input measurement, in a single forward pass of a neural network. We showcase the efficacy of our approach across diverse datasets and image restoration challenges, highlighting its prowess in uncertainty quantification and visualization. Our findings reveal that our method performs comparably to a baseline that hierarchically clusters samples from a diffusion-based posterior sampler, yet achieves this with orders of magnitude greater speed. Code and examples are available at our [webpage](https://eliasnehme.github.io/PosteriorTrees/).

Enhancing exploration in reinforcement learning (RL) through the incorporation of intrinsic rewards, specifically by leveraging *state discrepancy* measures within various metric spaces as exploration bonuses, has emerged as a prevalent strategy to encourage agents to visit novel states. The critical factor lies in how to quantify the difference between adjacent states as *novelty* for promoting effective exploration. Nonetheless, existing methods that evaluate state discrepancy in the latent space under $L_1$ or $L_2$ norm often depend on count-based episodic terms as scaling factors for exploration bonuses, significantly limiting their scalability. Additionally, methods that utilize the bisimulation metric for evaluating state discrepancies face a theory-practice gap due to improper approximations in metric learning, particularly struggling with *hard exploration* tasks. To overcome these challenges, we introduce the **E**ffective **M**etric-based **E**xploration-bonus (EME). EME critically examines and addresses the inherent limitations and approximation inaccuracies of current metric-based state discrepancy methods for exploration, proposing a robust metric for state discrepancy evaluation backed by comprehensive theoretical analysis. Furthermore, we propose the diversity-enhanced scaling factor integrated into the exploration bonus to be dynamically adjusted by the variance of prediction from an ensemble of reward models, thereby enhancing exploration effectiveness in particularly challenging scenarios. Extensive experiments are conducted on hard exploration tasks within Atari games, Minigrid, Robosuite, and Habitat, which illustrate our method's scalability to various scenarios. The project website can be found at https://sites.google.com/view/effective-metric-exploration.

In this paper, we study the contextual multinomial logit (MNL) bandit problem in which a learning agent sequentially selects an assortment based on contextual information, and user feedback follows an MNL choice model. There has been a significant discrepancy between lower and upper regret bounds, particularly regarding the maximum assortment size $K$. Additionally, the variation in reward structures between these bounds complicates the quest for optimality. Under uniform rewards, where all items have the same expected reward, we establish a regret lower bound of $\Omega(d\sqrt{\smash[b]{T/K}})$ and propose a constant-time algorithm, OFU-MNL+, that achieves a matching upper bound of $\tilde{\mathcal{O}}(d\sqrt{\smash[b]{T/K}})$. We also provide instance-dependent minimax regret bounds under uniform rewards. Under non-uniform rewards, we prove a lower bound of $\Omega(d\sqrt{T})$ and an upper bound of $\tilde{\mathcal{O}}(d\sqrt{T})$, also achievable by OFU-MNL+. Our empirical studies support these theoretical findings. To the best of our knowledge, this is the first work in the contextual MNL bandit literature to prove minimax optimality --- for either uniform or non-uniform reward setting --- and to propose a computationally efficient algorithm that achieves this optimality up to logarithmic factors.

Interactive-Grounded Learning (IGL) [Xie et al., 2021] is a powerful framework in which a learner aims at maximizing unobservable rewards through interacting with an environment and observing reward-dependent feedback on the taken actions. To deal with personalized rewards that are ubiquitous in applications such as recommendation systems, Maghakian et al. [2022] study a version of IGL with context-dependent feedback, but their algorithm does not come with theoretical guarantees. In this work, we consider the same problem and provide the first provably efficient algorithms with sublinear regret under realizability. Our analysis reveals that the step-function estimator of prior work can deviate uncontrollably due to finite-sample effects. Our solution is a novel Lipschitz reward estimator which underestimates the true reward and enjoys favorable generalization performances. Building on this estimator, we propose two algorithms, one based on explore-then-exploit and the other based on inverse-gap weighting. We apply IGL to learning from image feedback and learning from text feedback, which are reward-free settings that arise in practice. Experimental results showcase the importance of using our Lipschitz reward estimator and the overall effectiveness of our algorithms.

The ability to detect aerial objects with limited annotation is pivotal to the development of real-world aerial intelligence systems. In this work, we focus on a demanding but practical sparsely annotated object detection (SAOD) in aerial images, which encompasses a wider variety of aerial scenes with the same number of annotated objects. Although most existing SAOD methods rely on fixed thresholding to filter pseudo-labels for enhancing detector performance, adapting to aerial objects proves challenging due to the imbalanced probabilities/confidences associated with predicted aerial objects. To address this problem, we propose a novel Progressive Exploration-Conformal Learning (PECL) framework to address the SAOD task, which can adaptively perform the selection of high-quality pseudo-labels in aerial images. Specifically, the pseudo-label exploration can be formulated as a decision-making paradigm by adopting a conformal pseudo-label explorer and a multi-clue selection evaluator. The conformal pseudo-label explorer learns an adaptive policy by maximizing the cumulative reward, which can decide how to select these high-quality candidates by leveraging their essential characteristics and inter-instance contextual information. The multi-clue selection evaluator is designed to evaluate the explorer-guided pseudo-label selections by providing an instructive feedback for policy optimization. Finally, the explored pseudo-labels can be adopted to guide the optimization of aerial object detector in a closed-looping progressive fashion. Comprehensive evaluations on two public datasets demonstrate the superiority of our PECL when compared with other state-of-the-art methods in the sparsely annotated aerial object detection task.

We study the preference-based pure exploration problem for bandits with vector-valued rewards and a set of preferences imposed over them. Specifically, we aim to identify the most preferred policy over a set of arms according to the preferences induced on the reward vectors by an ordering cone $C$. First, to quantify the impact of preferences, we derive a novel lower bound on the sample complexity for identifying the most preferred arm with confidence level $1-\delta$. Our lower bound shows that how the geometry of the preferences and reward vectors changes the hardness of this problem. We further explicate this geometry for Gaussian distributions of rewards, and provide a convex reformulation of the lower bound solvable with linear programming. Then, we leverage this convex reformulation of the lower bound to design the Track and Stop with Preferences (TSwP) algorithm that identifies the most preferred policy. Finally, we derive a new concentration result for vector-valued rewards, and show that TSwP achieves a matching sample complexity upper bound.

This paper considers the problem of online learning with non-convex loss functions in dynamic environments. Recently, Suggala and Netrapalli [2020] demonstrated that follow the perturbed leader (FTPL) can achieve optimal regret for non-convex losses, but their results are limited to static environments. In this research, we examine dynamic environments and choose \emph{dynamic regret} and \emph{adaptive regret} to measure the performance. First, we propose an algorithm named FTPL-D by restarting FTPL periodically and establish $O(T^\frac{2}{3}(V_T+1)^\frac{1}{3})$ dynamic regret with the prior knowledge of $V_T$, which is the variation of loss functions. In the case that $V_T$ is unknown, we run multiple FTPL-D with different restarting parameters as experts and use a meta-algorithm to track the best one on the fly. To address the challenge of non-convexity, we utilize randomized sampling in the process of tracking experts. Next, we present a novel algorithm called FTPL-A that dynamically maintains a group of FTPL experts and combines them with an advanced meta-algorithm to obtain $O(\sqrt{\tau\log{T}})$ adaptive regret for any interval of length $\tau$. Moreover, we demonstrate that FTPL-A also attains an $\tilde{O}(T^\frac{2}{3}(V_T+1)^\frac{1}{3})$ dynamic regret bound. Finally, we discuss the application to online constrained meta-learning and conduct experiments to verify the effectiveness of our methods.

Traditional information theory provides a valuable foundation for Reinforcement Learning (RL), particularly through representation learning and entropy maximiza tion for agent exploration. However, existing methods primarily concentrate on modeling the uncertainty associated with RL’s random variables, neglecting the in herent structure within the state and action spaces. In this paper, we propose a novel Structural Information principles-based Effective Exploration framework, namely SI2E. Structural mutual information between two variables is defined to address the single-variable limitation in structural information, and an innovative embedding principle is presented to capture dynamics-relevant state-action representations. The SI2E analyzes value differences in the agent’s policy between state-action pairs and minimizes structural entropy to derive the hierarchical state-action struc ture, referred to as the encoding tree. Under this tree structure, value-conditional structural entropy is defined and maximized to design an intrinsic reward mechanism that avoids redundant transitions and promotes enhanced coverage in the state-action space. Theoretical connections are established between SI2E and classical information-theoretic methodologies, highlighting our framework’s rationality and advantage. Comprehensive evaluations in the MiniGrid, MetaWorld, and DeepMind Control Suite benchmarks demonstrate that SI2E significantly outperforms state-of-the-art exploration baselines regarding final performance and sample efficiency, with maximum improvements of 37.63% and 60.25%, respectively.