arXiv subjects

Benjamin Van Roy

Publications and source records attributed to Benjamin Van Roy.

At least 19 recordsLinked to original sources

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↗

arXiv2026

Reinforcement Learning with Pairwise Preferences in Long-Term Decision Problems

Reinforcement learning with scalar rewards is widely used for aligning machine-learning systems with user preferences. But, pairwise preferences are often more natural for users to specify than scalar rewards, and they express certain goals that scalar rewards cannot. Methods for reinforcement learning with pairwise preferences have thus received growing interest. Unfortunately, these methods are inefficient in problems with long time horizons, and they lack guarantees on the performance of Markov policies relative to history-dependent policies, which bridge the theory and practice of reinforcement learning. We address these limitations in a new problem setting for reinforcement learning with pairwise preferences called the \textit{Markov decision contest}. In this setting, we prove that stationary Markov policies perform just as well as history-dependent policies; that the problem of recovering an optimal policy exactly is in P; and that a simple iterative algorithm converges to an optimal policy at a sublinear rate. Lastly, we implement a deep-learning variant of our iterative algorithm and demonstrate its efficiency in long-term decision problems that require function approximation.

cs.LG↗

arXiv2026

Efficient Exploration at Scale

We develop an online learning algorithm that dramatically improves the data efficiency of reinforcement learning from human feedback (RLHF). Our algorithm incrementally updates reward and language models as choice data is received. The reward model is fit to the choice data, while the language model is updated by a variation of reinforce, with reinforcement signals provided by the reward model. Several features enable the efficiency gains: a small affirmative nudge added to each reinforcement signal, an epistemic neural network that models reward uncertainty, and information-directed exploration. With Gemma large language models (LLMs), our algorithm matches the performance of offline RLHF trained on 200K labels using fewer than 20K labels, representing more than a 10x gain in data efficiency. Extrapolating from our results, we expect our algorithm trained on 1M labels to match offline RLHF trained on 1B labels. This represents a 1,000x gain. To our knowledge, these are the first results to demonstrate that such large improvements are possible.

cs.LG↗

arXiv2026

Consequentialist Objectives and Catastrophe

Because human preferences are too complex to codify, AIs operate with misspecified objectives. Optimizing such objectives often produces undesirable outcomes; this phenomenon is known as reward hacking. Such outcomes are not necessarily catastrophic. Indeed, most examples of reward hacking in previous literature are benign. And typically, objectives can be modified to resolve the issue. We study the prospect of catastrophic outcomes induced by AIs operating in complex environments. We argue that, when capabilities are sufficiently advanced, pursuing a fixed consequentialist objective tends to result in catastrophic outcomes. We formalize this by establishing conditions that provably lead to such outcomes. Under these conditions, simple or random behavior is safe. Catastrophic risk arises due to extraordinary competence rather than incompetence. With a fixed consequentialist objective, avoiding catastrophe requires constraining AI capabilities. In fact, constraining capabilities the right amount not only averts catastrophe but yields valuable outcomes. Our results apply to any objective produced by modern industrial AI development pipelines.

cs.AI↗

arXiv2026

Prior Diffusiveness and Regret in the Linear-Gaussian Bandit

We prove that Thompson sampling exhibits $\tilde{O}(\sigma d \sqrt{T} + d r \sqrt{\mathrm{Tr}(\Sigma_0)})$ Bayesian regret in the linear-Gaussian bandit with a $\mathcal{N}(\mu_0, \Sigma_0)$ prior distribution on the coefficients, where $d$ is the dimension, $T$ is the time horizon, $r$ is the maximum $\ell_2$ norm of the actions, and $\sigma^2$ is the noise variance. In contrast to existing regret bounds, this shows that to within logarithmic factors, the prior-dependent ``burn-in'' term $d r \sqrt{\mathrm{Tr}(\Sigma_0)}$ decouples additively from the minimax (long run) regret $\sigma d \sqrt{T}$. Previous regret bounds exhibit a multiplicative dependence on these terms. We establish these results via a new ``elliptical potential'' lemma, and also provide a lower bound indicating that the burn-in term is unavoidable.

cs.LG↗

arXiv2025

Capacity-Constrained Continual Learning

Any agents we can possibly build are subject to capacity constraints, as memory and compute resources are inherently finite. However, comparatively little attention has been dedicated to understanding how agents with limited capacity should allocate their resources for optimal performance. The goal of this paper is to shed some light on this question by studying a simple yet relevant continual learning problem: the capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem. We derive a solution to this problem under appropriate technical conditions. Moreover, for problems that can be decomposed into a set of sub-problems, we also demonstrate how to optimally allocate capacity across these sub-problems in the steady state. We view the results of this paper as a first step in the systematic theoretical study of learning under capacity constraints.

cs.LG↗

arXiv2025

Granular feedback merits sophisticated aggregation

Human feedback is increasingly used across diverse applications like training AI models, developing recommender systems, and measuring public opinion -- with granular feedback often being preferred over binary feedback for its greater informativeness. While it is easy to accurately estimate a population's distribution of feedback given feedback from a large number of individuals, cost constraints typically necessitate using smaller groups. A simple method to approximate the population distribution is regularized averaging: compute the empirical distribution and regularize it toward a prior. Can we do better? As we will discuss, the answer to this question depends on feedback granularity. Suppose one wants to predict a population's distribution of feedback using feedback from a limited number of individuals. We show that, as feedback granularity increases, one can substantially improve upon predictions of regularized averaging by combining individuals' feedback in ways more sophisticated than regularized averaging. Our empirical analysis using questions on social attitudes confirms this pattern. In particular, with binary feedback, sophistication barely reduces the number of individuals required to attain a fixed level of performance. By contrast, with five-point feedback, sophisticated methods match the performance of regularized averaging with about half as many individuals.

cs.LG↗

arXiv2025

Misalignment from Treating Means as Ends

Reward functions, learned or manually specified, are rarely perfect. Instead of accurately expressing human goals, these reward functions are often distorted by human beliefs about how best to achieve those goals. Specifically, these reward functions often express a combination of the human's terminal goals -- those which are ends in themselves -- and the human's instrumental goals -- those which are means to an end. We formulate a simple example in which even slight conflation of instrumental and terminal goals results in severe misalignment: optimizing the misspecified reward function results in poor performance when measured by the true reward function. This example distills the essential properties of environments that make reinforcement learning highly sensitive to conflation of instrumental and terminal goals. We discuss how this issue can arise with a common approach to reward learning and how it can manifest in real environments.

cs.LG↗

arXiv2024

Choice Between Partial Trajectories: Disentangling Goals from Beliefs

As AI agents generate increasingly sophisticated behaviors, manually encoding human preferences to guide these agents becomes more challenging. To address this, it has been suggested that agents instead learn preferences from human choice data. This approach requires a model of choice behavior that the agent can use to interpret the data. For choices between partial trajectories of states and actions, previous models assume choice probabilities are determined by the partial return or the cumulative advantage. We consider an alternative model based instead on the bootstrapped return, which adds to the partial return an estimate of the future return. Benefits of the bootstrapped return model stem from its treatment of human beliefs. Unlike partial return, choices based on bootstrapped return reflect human beliefs about the environment. Further, while recovering the reward function from choices based on cumulative advantage requires that those beliefs are correct, doing so from choices based on bootstrapped return does not. To motivate the bootstrapped return model, we formulate axioms and prove an Alignment Theorem. This result formalizes how, for a general class of preferences, such models are able to disentangle goals from beliefs. This ensures recovery of an aligned reward function when learning from choices based on bootstrapped return. The bootstrapped return model also affords greater robustness to choice behavior. Even when choices are based on partial return, learning via a bootstrapped return model recovers an aligned reward function. The same holds with choices based on the cumulative advantage if the human and the agent both adhere to correct and consistent beliefs about the environment. On the other hand, if choices are based on bootstrapped return, learning via partial return or cumulative advantage models does not generally produce an aligned reward function.

cs.LG↗

arXiv2024

Aligning AI Agents via Information-Directed Sampling

The staggering feats of AI systems have brought to attention the topic of AI Alignment: aligning a "superintelligent" AI agent's actions with humanity's interests. Many existing frameworks/algorithms in alignment study the problem on a myopic horizon or study learning from human feedback in isolation, relying on the contrived assumption that the agent has already perfectly identified the environment. As a starting point to address these limitations, we define a class of bandit alignment problems as an extension of classic multi-armed bandit problems. A bandit alignment problem involves an agent tasked with maximizing long-run expected reward by interacting with an environment and a human, both involving details/preferences initially unknown to the agent. The reward of actions in the environment depends on both observed outcomes and human preferences. Furthermore, costs are associated with querying the human to learn preferences. Therefore, an effective agent ought to intelligently trade-off exploration (of the environment and human) and exploitation. We study these trade-offs theoretically and empirically in a toy bandit alignment problem which resembles the beta-Bernoulli bandit. We demonstrate while naive exploration algorithms which reflect current practices and even touted algorithms such as Thompson sampling both fail to provide acceptable solutions to this problem, information-directed sampling achieves favorable regret.

cs.LG↗

arXiv2024

The Need for a Big World Simulator: A Scientific Challenge for Continual Learning

The "small agent, big world" frame offers a conceptual view that motivates the need for continual learning. The idea is that a small agent operating in a much bigger world cannot store all information that the world has to offer. To perform well, the agent must be carefully designed to ingest, retain, and eject the right information. To enable the development of performant continual learning agents, a number of synthetic environments have been proposed. However, these benchmarks suffer from limitations, including unnatural distribution shifts and a lack of fidelity to the "small agent, big world" framing. This paper aims to formalize two desiderata for the design of future simulated environments. These two criteria aim to reflect the objectives and complexity of continual learning in practical settings while enabling rapid prototyping of algorithms on a smaller scale.

cs.LG↗

arXiv2024

Information-Theoretic Foundations for Machine Learning

The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact, practitioners have been able to guide their future experimentation via observations from previous large-scale empirical investigations. In this work, we propose a theoretical framework which attempts to provide rigor to existing practices in machine learning. To the theorist, we provide a framework which is mathematically rigorous and leaves open many interesting ideas for future exploration. To the practitioner, we provide a framework whose results are simple, and provide intuition to guide future investigations across a wide range of learning paradigms. Concretely, we provide a theoretical framework rooted in Bayesian statistics and Shannon's information theory which is general enough to unify the analysis of many phenomena in machine learning. Our framework characterizes the performance of an optimal Bayesian learner as it learns from a stream of experience. Unlike existing analyses that weaken with increasing data complexity, our theoretical tools provide accurate insights across diverse machine learning settings. Throughout this work, we derive theoretical results and demonstrate their generality by apply them to derive insights specific to settings. These settings range from learning from data which is independently and identically distributed under an unknown distribution, to data which is sequential, to data which exhibits hierarchical structure amenable to meta-learning, and finally to data which is not fully explainable under the learner's beliefs (misspecification). These results are particularly relevant as we strive to understand and overcome increasingly difficult machine learning challenges in this endlessly complex world.

stat.ML↗

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

Satisficing Exploration for Deep Reinforcement Learning

A default assumption in the design of reinforcement-learning algorithms is that a decision-making agent always explores to learn optimal behavior. In sufficiently complex environments that approach the vastness and scale of the real world, however, attaining optimal performance may in fact be an entirely intractable endeavor and an agent may seldom find itself in a position to complete the requisite exploration for identifying an optimal policy. Recent work has leveraged tools from information theory to design agents that deliberately forgo optimal solutions in favor of sufficiently-satisfying or satisficing solutions, obtained through lossy compression. Notably, such agents may employ fundamentally different exploratory decisions to learn satisficing behaviors more efficiently than optimal ones that are more data intensive. While supported by a rigorous corroborating theory, the underlying algorithm relies on model-based planning, drastically limiting the compatibility of these ideas with function approximation and high-dimensional observations. In this work, we remedy this issue by extending an agent that directly represents uncertainty over the optimal value function allowing it to both bypass the need for model-based planning and to learn satisficing policies. We provide simple yet illustrative experiments that demonstrate how our algorithm enables deep reinforcement-learning agents to achieve satisficing behaviors. In keeping with previous work on this setting for multi-armed bandits, we additionally find that our algorithm is capable of synthesizing optimal behaviors, when feasible, more efficiently than its non-information-theoretic counterpart.

cs.LG↗

arXiv2024

Information-Theoretic Foundations for Neural Scaling Laws

Neural scaling laws aim to characterize how out-of-sample error behaves as a function of model and training dataset size. Such scaling laws guide allocation of a computational resources between model and data processing to minimize error. However, existing theoretical support for neural scaling laws lacks rigor and clarity, entangling the roles of information and optimization. In this work, we develop rigorous information-theoretic foundations for neural scaling laws. This allows us to characterize scaling laws for data generated by a two-layer neural network of infinite width. We observe that the optimal relation between data and model size is linear, up to logarithmic factors, corroborating large-scale empirical investigations. Concise yet general results of the kind we establish may bring clarity to this topic and inform future investigations.

cs.LG↗

arXiv2024

Efficient Exploration for LLMs

We present evidence of substantial benefit from efficient exploration in gathering human feedback to improve large language models. In our experiments, an agent sequentially generates queries while fitting a reward model to the feedback received. Our best-performing agent generates queries using double Thompson sampling, with uncertainty represented by an epistemic neural network. Our results demonstrate that efficient exploration enables high levels of performance with far fewer queries. Further, both uncertainty estimation and the choice of exploration scheme play critical roles.

cs.LG↗

arXiv2024

Adaptive Crowdsourcing Via Self-Supervised Learning

Common crowdsourcing systems average estimates of a latent quantity of interest provided by many crowdworkers to produce a group estimate. We develop a new approach -- predict-each-worker -- that leverages self-supervised learning and a novel aggregation scheme. This approach adapts weights assigned to crowdworkers based on estimates they provided for previous quantities. When skills vary across crowdworkers or their estimates correlate, the weighted sum offers a more accurate group estimate than the average. Existing algorithms such as expectation maximization can, at least in principle, produce similarly accurate group estimates. However, their computational requirements become onerous when complex models, such as neural networks, are required to express relationships among crowdworkers. Predict-each-worker accommodates such complexity as well as many other practical challenges. We analyze the efficacy of predict-each-worker through theoretical and computational studies. Among other things, we establish asymptotic optimality as the number of engagements per crowdworker grows.

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↗