Pure Exploration with Feedback Graphs

We study the sample complexity of pure exploration in an online learning problem with a feedback graph. This graph dictates the feedback available to the learner, covering scenarios between full-information, pure bandit feedback, and settings with no feedback on the chosen action. While variants of this problem have been investigated for regret minimization, no prior work has addressed the pure exploration setting, which is the focus of our study. We derive an instance-specific lower bound on the sample complexity of learning the best action with fixed confidence, even when the feedback graph is unknown and stochastic, and present unidentifiability results for Bernoulli rewards. Additionally, our findings reveal how the sample complexity scales with key graph-dependent quantities. Lastly, we introduce TaS-FG (Track and Stop for Feedback Graphs), an asymptotically optimal algorithm, and demonstrate its efficiency across different graph configurations.

Language Model Personalization via Reward Factorization

Modern large language models (LLMs) are optimized for human-aligned responses using Reinforcement Learning from Human Feedback (RLHF). However, existing RLHF approaches assume a universal preference model and fail to account for individual user preferences, limiting their effectiveness in personalized applications. We introduce a framework that extends RLHF to enable user personalization by leveraging the assumption that user preferences lie in a low-dimensional space. Instead of training a separate model per user, we represent user-specific rewards as a linear combination of base reward functions. Using only ~10 user responses, our method can infer user-specific rewards and align LLM outputs accordingly. We validate our approach through experiments with both synthetic and real users, demonstrating significant personalization achieved by our method. In human evaluations, our method achieves a 67% win rate over default GPT-4o responses.

Adaptive Exploration for Multi-Reward Multi-Policy Evaluation

We study the policy evaluation problem in an online multi-reward multi-policy discounted setting, where multiple reward functions must be evaluated simultaneously for different policies. We adopt an $(\epsilon,\delta)$-PAC perspective to achieve $\epsilon$-accurate estimates with high confidence across finite or convex sets of rewards, a setting that has not been investigated in the literature. Building on prior work on Multi-Reward Best Policy Identification, we adapt the MR-NaS exploration scheme to jointly minimize sample complexity for evaluating different policies across different reward sets. Our approach leverages an instance-specific lower bound revealing how the sample complexity scales with a measure of value deviation, guiding the design of an efficient exploration policy. Although computing this bound entails a hard non-convex optimization, we propose an efficient convex approximation that holds for both finite and convex reward sets. Experiments in tabular domains demonstrate the effectiveness of this adaptive exploration scheme.

ORSO: Accelerating Reward Design via Online Reward Selection and Policy Optimization

Reward shaping is a critical component in reinforcement learning (RL), particularly for complex tasks where sparse rewards can hinder learning. While shaping rewards have been introduced to provide additional guidance, selecting effective shaping functions remains challenging and computationally expensive. This paper introduces Online Reward Selection and Policy Optimization (ORSO), a novel approach that frames shaping reward selection as an online model selection problem. ORSO employs principled exploration strategies to automatically identify promising shaping reward functions without human intervention, balancing exploration and exploitation with provable regret guarantees. We demonstrate ORSO's effectiveness across various continuous control tasks using the Isaac Gym simulator. Compared to traditional methods that fully evaluate each shaping reward function, ORSO significantly improves sample efficiency, reduces computational time, and consistently identifies high-quality reward functions that produce policies comparable to those generated by domain experts through hand-engineered rewards.

State-free Reinforcement Learning

In this work, we study the \textit{state-free RL} problem, where the algorithm does not have the states information before interacting with the environment. Specifically, denote the reachable state set by ${S}^\Pi := \{ s|\max_{\pi\in \Pi}q^{P, \pi}(s)>0 \}$, we design an algorithm which requires no information on the state space $S$ while having a regret that is completely independent of ${S}$ and only depend on ${S}^\Pi$. We view this as a concrete first step towards \textit{parameter-free RL}, with the goal of designing RL algorithms that require no hyper-parameter tuning.

Second Order Bounds for Contextual Bandits with Function Approximation

Many works have developed algorithms no-regret algorithms for contextual bandits with function approximation, where the mean rewards over context-action pairs belongs to a function class. Although there are many approaches to this problem, one that has gained in importance is the use of algorithms based on the optimism principle such as optimistic least squares. It can be shown the regret of this algorithm scales as square root of the product of the eluder dimension (a statistical measure of the complexity of the function class), the logarithm of the function class size and the time horizon. Unfortunately, even if the variance of the measurement noise of the rewards at each time is changing and is very small, the regret of the optimistic least squares algorithm scales with square root of the time horizon. In this work we are the first to develop algorithms that satisfy regret bounds of scaling not with the square root of the time horizon, but the square root of the sum of the measurement variances in the setting of contextual bandits with function approximation when the variances are unknown. These bounds generalize existing techniques for deriving second order bounds in contextual linear problems.

Learning Rate-Free Reinforcement Learning: A Case for Model Selection with Non-Stationary Objectives

The performance of reinforcement learning (RL) algorithms is sensitive to the choice of hyperparameters, with the learning rate being particularly influential. RL algorithms fail to reach convergence or demand an extensive number of samples when the learning rate is not optimally set. In this work, we show that model selection can help to improve the failure modes of RL that are due to suboptimal choices of learning rate. We present a model selection framework for Learning Rate-Free Reinforcement Learning that employs model selection methods to select the optimal learning rate on the fly. This approach of adaptive learning rate tuning neither depends on the underlying RL algorithm nor the optimizer and solely uses the reward feedback to select the learning rate; hence, the framework can input any RL algorithm and produce a learning rate-free version of it. We conduct experiments for policy optimization methods and evaluate various model selection strategies within our framework. Our results indicate that data-driven model selection algorithms are better alternatives to standard bandit algorithms when the optimal choice of hyperparameter is time-dependent and non-stationary.

Provable Interactive Learning with Hindsight Instruction Feedback

We study interactive learning in a setting where the agent has to generate a response (e.g., an action or trajectory) given a context and an instruction. In contrast, to typical approaches that train the system using reward or expert supervision on response, we study learning with hindsight instruction where a teacher provides an instruction that is most suitable for the agent's generated response. This hindsight labeling of instruction is often easier to provide than providing expert supervision of the optimal response which may require expert knowledge or can be impractical to elicit. We initiate the theoretical analysis of interactive learning with hindsight labeling. We first provide a lower bound showing that in general, the regret of any algorithm must scale with the size of the agent's response space. We then study a specialized setting where the underlying instruction-response distribution can be decomposed as a low-rank matrix. We introduce an algorithm called LORIL for this setting and show that its regret scales as $\sqrt{T}$ where $T$ is the number of rounds and depends on the intrinsic rank but does not depend on the size of the agent's response space. We provide experiments in two domains showing that LORIL outperforms baselines even when the low-rank assumption is violated.

Multiple-policy Evaluation via Density Estimation

In this work, we focus on the multiple-policy evaluation problem where we are given a set of $K$ target policies and the goal is to evaluate their performance (the expected total rewards) to an accuracy $\epsilon$ with probability at least $1-\delta$. We propose an algorithm named $\mathrm{CAESAR}$ to address this problem. Our approach is based on computing an approximate optimal offline sampling distribution and using the data sampled from it to perform the simultaneous estimation of the policy values. $\mathrm{CAESAR}$ consists of two phases. In the first one we produce coarse estimates of the vistation distributions of the target policies at a low order sample complexity rate that scales with $\tilde{O}(\frac{1}{\epsilon})$. In the second phase, we approximate the optimal offline sampling distribution and compute the importance weighting ratios for all target policies by minimizing a step-wise quadratic loss function inspired by the objective in DualDICE. Up to low order and logarithm terms $\mathrm{CAESAR}$ achieves a sample complexity $\tilde{O}\left(\frac{H^4}{\epsilon^2}\sum_{h=1}^H\max_{k\in[K]}\sum_{s,a}\frac{(d_h^{\pi^k}(s,a))^2}{\mu^*_h(s,a)}\right)$, where $d^{\pi}$ is the visitation distribution of policy $\pi$ and $\mu^*$ is the optimal sampling distribution.

Provably Sample Efficient RLHF via Active Preference Optimization

Reinforcement Learning from Human Feedback (RLHF) is pivotal in aligning Large Language Models (LLMs) with human preferences. While these aligned generative models have demonstrated impressive capabilities across various tasks, the dependence on high-quality human preference data poses a costly bottleneck in practical implementation of RLHF. Hence better and adaptive strategies for data collection is needed. To this end, we frame RLHF as a contextual preference bandit problem with prompts as contexts and show that the naive way of collecting preference data by choosing prompts uniformly at random leads to a policy that suffers an $\Omega(1)$ suboptimality gap in rewards. Then we propose $\textit{Active Preference Optimization}$ ($\texttt{APO}$), an algorithm that actively selects prompts to collect preference data. Under the Bradley-Terry-Luce (BTL) preference model, \texttt{APO} achieves sample efficiency without compromising on policy performance. We show that given a sample budget of $T$, the suboptimality gap of a policy learned via $\texttt{APO}$ scales as $O(1/\sqrt{T})$. Next, we propose a compute-efficient batch version of $\texttt{APO}$ with minor modification and evaluate its performance in practice. Experimental evaluations on a human preference dataset validate \texttt{APO}'s efficacy as a sample-efficient and practical solution to data collection for RLHF, facilitating alignment of LLMs with human preferences in a cost-effective and scalable manner.