arXiv subjects

Wanqiao Xu

Publications and source records attributed to Wanqiao Xu.

12 recordsLinked to original sources

arXiv2026

Formalizing Learning from Language Feedback with Provable Guarantees

Interactively learning from observation and language feedback is an increasingly studied area driven by the emergence of large language model (LLM) agents. Despite impressive empirical demonstrations, so far a principled framing of these decision problems remains lacking. We formalize the Learning from Language Feedback (LLF) problem, assert sufficient assumptions to enable learning despite latent rewards, and introduce $\textit{transfer eluder dimension}$ as a measure to characterize the hardness of LLF. We formalize the intuition that information in the language feedback governs the learning complexity, and demonstrate cases where learning from rich language feedback can be exponentially faster than learning from reward. We develop a no-regret algorithm, called $\texttt{HELiX}$, that provably solves LLF problems through sequential interactions, with performance guarantees that scale with the transfer eluder dimension. Across several empirical domains, we show that $\texttt{HELiX}$ performs well even when repeatedly prompting LLMs does not work reliably. Our contributions mark an important step towards designing principled interactive learning algorithms using generic language feedback.

cs.LG↗

arXiv2026

An Information-Theoretic Definition for Open-Ended Learning

A growing body of work points to the great promise of AI systems that can continually expand their capabilities as they operate in an open-ended environment. But yet there is no coherent definition of open-endedness or theory about how an agent ought to explore an open-ended environment. We introduce an information-theoretic definition based on a new concept -- the ${\textit bit-equivalent}$ -- which quantifies the information required to attain each level of expected reward. We consider an environment to be open-ended if an agent can attain linear growth in the bit-equivalent. We establish that classical bandit environments are not open-ended and formulate a bandit environment that is. We also introduce an algorithm that achieves open-ended learning in this environment.

cs.LG↗

arXiv2025

Posterior Sampling for Continuing Environments

We develop an extension of posterior sampling for reinforcement learning (PSRL) that is suited for a continuing agent-environment interface and integrates naturally into agent designs that scale to complex environments. The approach, continuing PSRL, maintains a statistically plausible model of the environment and follows a policy that maximizes expected $γ$-discounted return in that model. At each time, with probability $1-γ$, the model is replaced by a sample from the posterior distribution over environments. For a choice of discount factor that suitably depends on the horizon $T$, we establish an $\tilde{O}(τS \sqrt{A T})$ bound on the Bayesian regret, where $S$ is the number of environment states, $A$ is the number of actions, and $τ$ denotes the reward averaging time, which is a bound on the duration required to accurately estimate the average reward of any policy. Our work is the first to formalize and rigorously analyze the resampling approach with randomized exploration.

cs.LG↗

arXiv2025

On Aligning Prediction Models with Clinical Experiential Learning: A Prostate Cancer Case Study

Over the past decade, the use of machine learning (ML) models in healthcare applications has rapidly increased. Despite high performance, modern ML models do not always capture patterns the end user requires. For example, a model may predict a non-monotonically decreasing relationship between cancer stage and survival, keeping all other features fixed. In this paper, we present a reproducible framework for investigating this misalignment between model behavior and clinical experiential learning, focusing on the effects of underspecification of modern ML pipelines. In a prostate cancer outcome prediction case study, we first identify and address these inconsistencies by incorporating clinical knowledge, collected by a survey, via constraints into the ML model, and subsequently analyze the impact on model performance and behavior across degrees of underspecification. The approach shows that aligning the ML model with clinical experiential learning is possible without compromising performance. Motivated by recent literature in generative AI, we further examine the feasibility of a feedback-driven alignment approach in non-generative AI clinical risk prediction models through a randomized experiment with clinicians. Our findings illustrate that, by eliciting clinicians' model preferences using our proposed methodology, the larger the difference in how the constrained and unconstrained models make predictions for a patient, the more apparent the difference is in clinical interpretation.

cs.LG↗

arXiv2024

Pearl: A Production-ready Reinforcement Learning Agent

Reinforcement learning (RL) is a versatile framework for optimizing long-term goals. Although many real-world problems can be formalized with RL, learning and deploying a performant RL policy requires a system designed to address several important challenges, including the exploration-exploitation dilemma, partial observability, dynamic action spaces, and safety concerns. While the importance of these challenges has been well recognized, existing open-source RL libraries do not explicitly address them. This paper introduces Pearl, a Production-Ready RL software package designed to embrace these challenges in a modular way. In addition to presenting benchmarking results, we also highlight examples of Pearl's ongoing industry adoption to demonstrate its advantages for production use cases. Pearl is open sourced on GitHub at github.com/facebookresearch/pearl and its official website is pearlagent.github.io.

cs.LG↗

arXiv2024

Exploration Unbound

A sequential decision-making agent balances between exploring to gain new knowledge about an environment and exploiting current knowledge to maximize immediate reward. For environments studied in the traditional literature, optimal decisions gravitate over time toward exploitation as the agent accumulates sufficient knowledge and the benefits of further exploration vanish. What if, however, the environment offers an unlimited amount of useful knowledge and there is large benefit to further exploration no matter how much the agent has learned? We offer a simple, quintessential example of such a complex environment. In this environment, rewards are unbounded and an agent can always increase the rate at which rewards accumulate by exploring to learn more. Consequently, an optimal agent forever maintains a propensity to explore.

cs.LG↗

arXiv2024

RLHF and IIA: Perverse Incentives

Existing algorithms for reinforcement learning from human feedback (RLHF) can incentivize responses at odds with preferences because they are based on models that assume independence of irrelevant alternatives (IIA). The perverse incentives induced by IIA hinder innovations on query formats and learning algorithms.

cs.LG↗

arXiv2023

Shattering the Agent-Environment Interface for Fine-Tuning Inclusive Language Models

A centerpiece of the ever-popular reinforcement learning from human feedback (RLHF) approach to fine-tuning autoregressive language models is the explicit training of a reward model to emulate human feedback, distinct from the language model itself. This reward model is then coupled with policy-gradient methods to dramatically improve the alignment between language model outputs and desired responses. In this work, we adopt a novel perspective wherein a pre-trained language model is itself simultaneously a policy, reward function, and transition function. An immediate consequence of this is that reward learning and language model fine-tuning can be performed jointly and directly, without requiring any further downstream policy optimization. While this perspective does indeed break the traditional agent-environment interface, we nevertheless maintain that there can be enormous statistical benefits afforded by bringing to bear traditional algorithmic concepts from reinforcement learning. Our experiments demonstrate one concrete instance of this through efficient exploration based on the representation and resolution of epistemic uncertainty. In order to illustrate these ideas in a transparent manner, we restrict attention to a simple didactic data generating process and leave for future work extension to systems of practical scale.

cs.CL↗

arXiv2023

Uniformly Conservative Exploration in Reinforcement Learning

A key challenge to deploying reinforcement learning in practice is avoiding excessive (harmful) exploration in individual episodes. We propose a natural constraint on exploration -- \textit{uniformly} outperforming a conservative policy (adaptively estimated from all data observed thus far), up to a per-episode exploration budget. We design a novel algorithm that uses a UCB reinforcement learning policy for exploration, but overrides it as needed to satisfy our exploration constraint with high probability. Importantly, to ensure unbiased exploration across the state space, our algorithm adaptively determines when to explore. We prove that our approach remains conservative while minimizing regret in the tabular setting. We experimentally validate our results on a sepsis treatment task and an HIV treatment task, demonstrating that our algorithm can learn while ensuring good performance compared to the baseline policy for every patient; the latter task also demonstrates that our approach extends to continuous state spaces via deep reinforcement learning.

cs.LG↗

arXiv2021

Distribution of Eigenvalues of Matrix Ensembles arising from Wigner and Palindromic Toeplitz Blocks

Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions; this correspondence has allowed RMT to successfully predict many number theoretic behaviors. However there are some operations which to date have no RMT analogue. Our motivation is to find an RMT analogue of Rankin-Selberg convolution, which constructs a new $L$-functions from an input pair. We report one such attempt; while it does not appear to model convolution, it does create new ensembles with properties hybridizing those of its constituents. For definiteness we concentrate on the ensemble of palindromic real symmetric Toeplitz (PST) matrices and the ensemble of real symmetric matrices, whose limiting spectral measures are the Gaussian and semi-circular distributions, respectively; these were chosen as they are the two extreme cases in terms of moment calculations. For a PST matrix $A$ and a real symmetric matrix $B$, we construct an ensemble of random real symmetric block matrices whose first row is $\lbrace A, B \rbrace$ and whose second row is $\lbrace B, A \rbrace$. By Markov's Method of Moments and the use of free probability, we show this ensemble converges weakly and almost surely to a new, universal distribution with a hybrid of Gaussian and semi-circular behaviors. We extend this construction by considering an iterated concatenation of matrices from an arbitrary pair of random real symmetric sub-ensembles with different limiting spectral measures. We prove that finite iterations converge to new, universal distributions with hybrid behavior, and that infinite iterations converge to the limiting spectral measure of the dominant component matrix.

math.PR↗

arXiv2019

Gaps of Summands of the Zeckendorf Lattice

A beautiful theorem of Zeckendorf states that every positive integer has a unique decomposition as a sum of non-adjacent Fibonacci numbers. Such decompositions exist more generally, and much is known about them. First, for any positive linear recurrence {Gn} the number of summands in the legal decompositions for integers in [Gn, Gn+1) converges to a Gaussian distribution. Second, Bower, Insoft, Li, Miller, and Tosteson proved that the probability of a gap between summands in a decomposition which is larger than the recurrence length converges to geometric decay. While most of the literature involves one-dimensional sequences, some recent work by Chen, Guo, Jiang, Miller, Siktar, and Yu have extended these decompositions to d-dimensional lattices, where a legal decomposition is a chain of points such that one moves in all d dimensions to get from one point to the next. They proved that some but not all properties from 1-dimensional sequences still hold. We continue this work and look at the distribution of gaps between terms of legal decompositions, and prove similar to the 1-dimensional cases that when d = 2 the gap vectors converge to a bivariate geometric random variable.

math.NT↗

arXiv2019

Distribution of Eigenvalues of Random Real Symmetric Block Matrices

Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions. Many statistics in one can be interpreted in terms of quantities of the other; for example, zeros of $L$-functions correspond to eigenvalues of matrices, and values of $L$-functions to values of the characteristic polynomials. This correspondence has allowed RMT to successfully predict many number theory behaviors; however, there are some operations which to date have no RMT analogue. The motivation of this paper is to try and find an RMT equivalent to Rankin-Selberg convolution, which builds a new $L$-functions from an input pair. For definiteness we concentrate on two specific families, the ensemble of palindromic real symmetric Toeplitz (PST) matrices and the ensemble of real symmetric (RS) matrices, whose limiting spectral measures are the Gaussian and semicircle distributions, respectively; these were chosen as they are the two extreme cases in terms of moment calculations. For a PST matrix $A$ and a RS matrix $B$, we construct an ensemble of random real symmetric block matrices whose first row is $\lbrace A, B \rbrace$ and whose second row is $\lbrace B, A \rbrace$. By Markov's Method of Moments, we show this ensemble converges weakly and almost surely to a new, universal distribution with a hybrid of Gaussian and semicircle behaviors. We extend this construction by considering an iterated concatenation of matrices from an arbitrary pair of random real symmetric sub-ensembles with different limiting spectral measures. We prove that finite iterations converge to new, universal distributions with hybrid behavior, and that infinite iterations converge to the limiting spectral measures of the component matrices.

math.PR↗