arXiv subjects

Aldo Pacchiano

Publications and source records attributed to Aldo Pacchiano.

At least 37 records · Page 2Linked to original sources

arXiv2025

On the Hardness of Bandit Learning

We study the task of bandit learning, also known as best-arm identification, under the assumption that the true reward function f belongs to a known, but arbitrary, function class F. We seek a general theory of bandit learnability, akin to the PAC framework for classification. Our investigation is guided by the following two questions: (1) which classes F are learnable, and (2) how they are learnable. For example, in the case of binary PAC classification, learnability is fully determined by a combinatorial dimension - the VC dimension- and can be attained via a simple algorithmic principle, namely, empirical risk minimization (ERM). In contrast to classical learning-theoretic results, our findings reveal limitations of learning in structured bandits, offering insights into the boundaries of bandit learnability. First, for the question of "which", we show that the paradigm of identifying the learnable classes via a dimension-like quantity fails for bandit learning. We give a simple proof demonstrating that no combinatorial dimension can characterize bandit learnability, even in finite classes, following a standard definition of dimension introduced by Ben-David et al. (2019). For the question of "how", we prove a computational hardness result: we construct a reward function class for which at most two queries are needed to find the optimal action, yet no algorithm can do so in polynomial time unless RP=NP. We also prove that this class admits efficient algorithms for standard algorithmic operations often considered in learning theory, such as an ERM. This implies that computational hardness is in this case inherent to the task of bandit learning. Beyond these results, we investigate additional themes such as learning under noise, trade-offs between noise models, and the relationship between query complexity and regret minimization.

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arXiv2025

Active Preference Optimization for Sample Efficient RLHF

Large Language Models (LLMs) aligned using Reinforcement Learning from Human Feedback (RLHF) have shown remarkable generation abilities in numerous tasks. However, collecting high-quality human preferences creates costly bottlenecks in practical deployments, and hence, training data are often budgeted. In these scenarios, it is crucial to collect training data (e.g., contexts, a pair of generations for each context, and a preference indicating which generation is better) carefully, yet most of the existing methods sample contexts uniformly at random from a given collection. Given this, under the Bradley-Terry-Luce preference model and with a small budget of training data, we show that uniform sampling of contexts could lead to a policy (i.e., an aligned model) that suffers a constant sub-optimality gap from the optimal policy. This highlights the need for an adaptive context sampling strategy for effective alignment under a small sample budget. To address this, we reformulate RLHF within the contextual preference bandit framework, treating generations as actions, and give a nearly complete characterization of the sub-optimality gap in terms of both lower and upper bounds. First, when the action set is a $d$-dimensional hypercube and the number of samples is $T$, we show an $Ω(d/\sqrt{T})$ lower bound. Next, we propose an algorithm, $\textit{Active Preference Optimization}$ ($\texttt{APO}$), that iteratively collects preferences for the most uncertain contexts. We show that the sub-optimality gap of the policy learned via $\texttt{APO}$ matches the lower bound up to a log factor and a non-linearity constant. Finally, we perform experiments on practical datasets to validate $\texttt{APO}$'s efficacy over existing methods, establishing it as a sample-efficient and cost-effective solution for LLM alignment.

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arXiv2025

Second Order Bounds for Contextual Bandits with Function Approximation

Many works have developed no-regret algorithms for contextual bandits with function approximation, where the mean reward function 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.

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arXiv2025

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.

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arXiv2025

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.

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arXiv2025

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

Reward shaping is critical in reinforcement learning (RL), particularly for complex tasks where sparse rewards can hinder learning. However, choosing effective shaping rewards from a set of reward functions in a computationally efficient manner remains an open challenge. We propose Online Reward Selection and Policy Optimization (ORSO), a novel approach that frames the selection of shaping reward function as an online model selection problem. ORSO automatically identifies performant shaping reward functions without human intervention with provable regret guarantees. We demonstrate ORSO's effectiveness across various continuous control tasks. Compared to prior approaches, ORSO significantly reduces the amount of data required to evaluate a shaping reward function, resulting in superior data efficiency and a significant reduction in computational time (up to 8 times). ORSO consistently identifies high-quality reward functions outperforming prior methods by more than 50% and on average identifies policies as performant as the ones learned using manually engineered reward functions by domain experts.

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arXiv2024

A Theoretical Framework for Partially Observed Reward-States in RLHF

The growing deployment of reinforcement learning from human feedback (RLHF) calls for a deeper theoretical investigation of its underlying models. The prevalent models of RLHF do not account for neuroscience-backed, partially-observed "internal states" that can affect human feedback, nor do they accommodate intermediate feedback during an interaction. Both of these can be instrumental in speeding up learning and improving alignment. To address these limitations, we model RLHF as reinforcement learning with partially observed reward-states (PORRL). We accommodate two kinds of feedback $-$ cardinal and dueling feedback. We first demonstrate that PORRL subsumes a wide class of RL problems, including traditional RL, RLHF, and reward machines. For cardinal feedback, we present two model-based methods (POR-UCRL, POR-UCBVI). We give both cardinal regret and sample complexity guarantees for the methods, showing that they improve over naive history-summarization. We then discuss the benefits of a model-free method like GOLF with naive history-summarization in settings with recursive internal states and dense intermediate feedback. For this purpose, we define a new history aware version of the Bellman-eluder dimension and give a new guarantee for GOLF in our setting, which can be exponentially sharper in illustrative examples. For dueling feedback, we show that a naive reduction to cardinal feedback fails to achieve sublinear dueling regret. We then present the first explicit reduction that converts guarantees for cardinal regret to dueling regret. In both feedback settings, we show that our models and guarantees generalize and extend existing ones.

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arXiv2024

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 ${S}^Π:= \{ s|\max_{π\in Π}q^{P, π}(s)>0 \}$, 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 ${S}^Π$. 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.

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arXiv2024

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.

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arXiv2024

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.

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arXiv2024

Improving Offline RL by Blending Heuristics

We propose Heuristic Blending (HUBL), a simple performance-improving technique for a broad class of offline RL algorithms based on value bootstrapping. HUBL modifies the Bellman operators used in these algorithms, partially replacing the bootstrapped values with heuristic ones that are estimated with Monte-Carlo returns. For trajectories with higher returns, HUBL relies more on the heuristic values and less on bootstrapping; otherwise, it leans more heavily on bootstrapping. HUBL is very easy to combine with many existing offline RL implementations by relabeling the offline datasets with adjusted rewards and discount factors. We derive a theory that explains HUBL's effect on offline RL as reducing offline RL's complexity and thus increasing its finite-sample performance. Furthermore, we empirically demonstrate that HUBL consistently improves the policy quality of four state-of-the-art bootstrapping-based offline RL algorithms (ATAC, CQL, TD3+BC, and IQL), by 9% on average over 27 datasets of the D4RL and Meta-World benchmarks.

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arXiv2024

Data-Driven Online Model Selection With Regret Guarantees

We consider model selection for sequential decision making in stochastic environments with bandit feedback, where a meta-learner has at its disposal a pool of base learners, and decides on the fly which action to take based on the policies recommended by each base learner. Model selection is performed by regret balancing but, unlike the recent literature on this subject, we do not assume any prior knowledge about the base learners like candidate regret guarantees; instead, we uncover these quantities in a data-driven manner. The meta-learner is therefore able to leverage the realized regret incurred by each base learner for the learning environment at hand (as opposed to the expected regret), and single out the best such regret. We design two model selection algorithms operating with this more ambitious notion of regret and, besides proving model selection guarantees via regret balancing, we experimentally demonstrate the compelling practical benefits of dealing with actual regrets instead of candidate regret bounds.

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arXiv2024

Experiment Planning with Function Approximation

We study the problem of experiment planning with function approximation in contextual bandit problems. In settings where there is a significant overhead to deploying adaptive algorithms -- for example, when the execution of the data collection policies is required to be distributed, or a human in the loop is needed to implement these policies -- producing in advance a set of policies for data collection is paramount. We study the setting where a large dataset of contexts but not rewards is available and may be used by the learner to design an effective data collection strategy. Although when rewards are linear this problem has been well studied, results are still missing for more complex reward models. In this work we propose two experiment planning strategies compatible with function approximation. The first is an eluder planning and sampling procedure that can recover optimality guarantees depending on the eluder dimension of the reward function class. For the second, we show that a uniform sampler achieves competitive optimality rates in the setting where the number of actions is small. We finalize our results introducing a statistical gap fleshing out the fundamental differences between planning and adaptive learning and provide results for planning with model selection.

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arXiv2023

Anytime Model Selection in Linear Bandits

Model selection in the context of bandit optimization is a challenging problem, as it requires balancing exploration and exploitation not only for action selection, but also for model selection. One natural approach is to rely on online learning algorithms that treat different models as experts. Existing methods, however, scale poorly ($\text{poly}M$) with the number of models $M$ in terms of their regret. Our key insight is that, for model selection in linear bandits, we can emulate full-information feedback to the online learner with a favorable bias-variance trade-off. This allows us to develop ALEXP, which has an exponentially improved ($\log M$) dependence on $M$ for its regret. ALEXP has anytime guarantees on its regret, and neither requires knowledge of the horizon $n$, nor relies on an initial purely exploratory stage. Our approach utilizes a novel time-uniform analysis of the Lasso, establishing a new connection between online learning and high-dimensional statistics.

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arXiv2023

Unbiased Decisions Reduce Regret: Adversarial Domain Adaptation for the Bank Loan Problem

In many real world settings binary classification decisions are made based on limited data in near real-time, e.g. when assessing a loan application. We focus on a class of these problems that share a common feature: the true label is only observed when a data point is assigned a positive label by the principal, e.g. we only find out whether an applicant defaults if we accepted their loan application. As a consequence, the false rejections become self-reinforcing and cause the labelled training set, that is being continuously updated by the model decisions, to accumulate bias. Prior work mitigates this effect by injecting optimism into the model, however this comes at the cost of increased false acceptance rate. We introduce adversarial optimism (AdOpt) to directly address bias in the training set using adversarial domain adaptation. The goal of AdOpt is to learn an unbiased but informative representation of past data, by reducing the distributional shift between the set of accepted data points and all data points seen thus far. AdOpt significantly exceeds state-of-the-art performance on a set of challenging benchmark problems. Our experiments also provide initial evidence that the introduction of adversarial domain adaptation improves fairness in this setting.

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arXiv2023

Leveraging Offline Data in Online Reinforcement Learning

Two central paradigms have emerged in the reinforcement learning (RL) community: online RL and offline RL. In the online RL setting, the agent has no prior knowledge of the environment, and must interact with it in order to find an $ε$-optimal policy. In the offline RL setting, the learner instead has access to a fixed dataset to learn from, but is unable to otherwise interact with the environment, and must obtain the best policy it can from this offline data. Practical scenarios often motivate an intermediate setting: if we have some set of offline data and, in addition, may also interact with the environment, how can we best use the offline data to minimize the number of online interactions necessary to learn an $ε$-optimal policy? In this work, we consider this setting, which we call the \textsf{FineTuneRL} setting, for MDPs with linear structure. We characterize the necessary number of online samples needed in this setting given access to some offline dataset, and develop an algorithm, \textsc{FTPedel}, which is provably optimal, up to $H$ factors. We show through an explicit example that combining offline data with online interactions can lead to a provable improvement over either purely offline or purely online RL. Finally, our results illustrate the distinction between \emph{verifiable} learning, the typical setting considered in online RL, and \emph{unverifiable} learning, the setting often considered in offline RL, and show that there is a formal separation between these regimes.

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arXiv2023

Supervised Pretraining Can Learn In-Context Reinforcement Learning

Large transformer models trained on diverse datasets have shown a remarkable ability to learn in-context, achieving high few-shot performance on tasks they were not explicitly trained to solve. In this paper, we study the in-context learning capabilities of transformers in decision-making problems, i.e., reinforcement learning (RL) for bandits and Markov decision processes. To do so, we introduce and study Decision-Pretrained Transformer (DPT), a supervised pretraining method where the transformer predicts an optimal action given a query state and an in-context dataset of interactions, across a diverse set of tasks. This procedure, while simple, produces a model with several surprising capabilities. We find that the pretrained transformer can be used to solve a range of RL problems in-context, exhibiting both exploration online and conservatism offline, despite not being explicitly trained to do so. The model also generalizes beyond the pretraining distribution to new tasks and automatically adapts its decision-making strategies to unknown structure. Theoretically, we show DPT can be viewed as an efficient implementation of Bayesian posterior sampling, a provably sample-efficient RL algorithm. We further leverage this connection to provide guarantees on the regret of the in-context algorithm yielded by DPT, and prove that it can learn faster than algorithms used to generate the pretraining data. These results suggest a promising yet simple path towards instilling strong in-context decision-making abilities in transformers.

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arXiv2023

A Unified Model and Dimension for Interactive Estimation

We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called dissimilarity dimension which largely captures learnability in our model. We present a simple, general, and broadly-applicable algorithm, for which we obtain both regret and PAC generalization bounds that are polynomial in the new dimension. We show that our framework subsumes and thereby unifies two classic learning models: statistical-query learning and structured bandits. We also delineate how the dissimilarity dimension is related to well-known parameters for both frameworks, in some cases yielding significantly improved analyses.

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