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Aaron Roth

Publications and source records attributed to Aaron Roth.

At least 19 recordsLinked to original sources
arXiv2026

Defensive Boosting for Online Probabilistic Forecasting

We study online probabilistic forecasting of binary outcomes chosen by an adaptive adversary. Given an online learning algorithm for a weak hypothesis class $H$, we would like to efficiently obtain two incomparable guarantees that existing online boosting techniques provide separately. Online gradient boosting competes in Brier score with the best predictor induced by the span of $H$ on every sequence, but promises nothing when the span does not contain an accurate predictor. Online weak-to-strong boosting drives classification error to zero under a weak-learning condition, but promises little when that condition fails. We give a simple defensive forecasting algorithm, the Defensive Booster, that obtains both guarantees. On every adaptive sequence, its Brier score is competitive with the best prediction induced by the span of $H$ at the same rate as online gradient boosting; simultaneously, whenever the realized transcript satisfies the smooth weak-learning condition, its Brier score and randomized classification error satisfy the same rate guarantee as online classification boosting. This is achieved by operationalizing the "dual view" of boosting: When the algorithm's randomized classification error is persistently high, its mistake weights form a smooth reweighting on which every weak hypothesis has low edge, yielding an ex-post hard-core certificate that the weak-learning condition fails. We also develop a strongly adaptive variant, which satisfies both guarantees on every time interval. The Defensive Booster is very efficient: it accesses just one weak-class learner, whereas the prior online boosting methods we compare against maintain large weak-learner ensembles. Experiments on synthetic and real data streams demonstrate its strong predictive performance (sometimes substantially improving over all prior baselines) coupled with orders-of-magnitude faster runtime.

cs.LG↗
arXiv2026

Optimal Deterministic Multicalibration and Omniprediction

A model is multicalibrated on a collection of group weights $G$ if it is calibrated -- i.e. unbiased even conditional on its prediction -- not just overall, but also after reweighting contexts by each $g \in G$. It is a useful property for many downstream applications and is a basic desideratum of trustworthy machine learning. Before this work, all predictors known to attain the minimax-optimal $\widetilde O(\varepsilon^{-3})$ sample complexity rate for $\varepsilon$-multicalibration were randomized, while deterministic predictors were known only with substantially worse sample complexity. Whether randomization is necessary for optimal sample complexity in multicalibration was explicitly asked by [CLNR26] and implicitly in several prior works. We resolve this open problem by giving a minimax-optimal multicalibration algorithm that outputs a deterministic predictor. We then generalize the algorithm to produce optimal deterministic predictors that satisfy outcome indistinguishability (OI) with respect to finite or finitely covered collections of tests. As an application, this also gives deterministic omnipredictors and panpredictors with optimal sample complexity, resolving open problems posed by [OKK25] and [BHHLZ25].

cs.LG↗
arXiv2026

What Fits (Into Few Tokens) Doesn't Overfit: Compression and Generalization in ML Research Agents

Reusing a held-out benchmark adaptively should, in principle, invite overfitting. Yet benchmark-driven machine learning (ML) has produced surprisingly little overfitting in practice. An attractive hypothesis is that successful ML strategies are highly compressible. We study this in the setting of LLM-driven research agents, where the hypothesis becomes directly testable via two complementary information bottlenecks. In \emph{output compression}, an exploration agent adaptively searches for high-performance models using a validation set, and we test whether a fresh ``reproducer agent'' can reproduce its performance given only an extremely short prompt and the training data. In \emph{input compression}, the explorer receives only one-bit feedback indicating whether each submitted model improves on the running best. Across 8 datasets spanning tabular classification, vision, language modeling, diffusion modeling, and reward modeling, we find that these bottlenecks have little effect on performance: short prompts and compressible feedback are sufficient to reproduce and find high-performance models. The hypothesis is falsifiable: when we deliberately induce validation-set overfitting, the results fail to reproduce with short prompts. Taken together, our results support a description-length explanation for the lack of overfitting in benchmark-driven ML: successful strategies occupy a low-complexity region of strategy space.

cs.AI↗
arXiv2026

Rejoinder: The ICML 2023 Ranking Experiment: Examining Author Self-Assessment in ML/AI Peer Review

This article is the rejoinder to ``The ICML 2023 Ranking Experiment: Examining Author Self-Assessment in ML/AI Peer Review,'' to appear in the Journal of the American Statistical Association with discussion. To address the practical and theoretical points raised by the discussants, we organize our response around four core themes: (i) formulating peer review as a statistical estimation problem; (ii) mitigating equity and strategic concerns in the deployment of the Isotonic Mechanism; (iii) incorporating complementary signals such as reviewer rankings and structured metadata; and (iv) exploring a human-centered framework for peer review in the era of generative AI.

stat.AP↗
arXiv2026

Instance-Adaptive Online Multicalibration

We study online multicalibration beyond the worst-case. We give a single, efficient algorithm which dynamically interpolates between benign and worst-case sequences by adaptively refining a dyadic grid of prediction values. Its error is controlled by the number of leaves in the refinement tree. Our analysis recovers the known $\widetilde O(T^{2/3})$ worst-case-optimal rate for online multicalibration, while simultaneously automatically adapting to easier instances: in the marginal stochastic setting it obtains a rate of $\widetilde O(\sqrt T)$, and for piecewise-stationary means with $J$ segments its rate is $\widetilde O(\sqrt{JT})$. More generally, the rate depends on a threshold-complexity measure of the predictable mean process relative to the group family. We show that this dependence is tight up to logarithmic factors.

cs.LG↗
arXiv2026

The Sample Complexity of Multicalibration

We study the minimax sample complexity of multicalibration in the batch setting. A learner observes $n$ i.i.d. samples from an unknown distribution and must output a (possibly randomized) predictor whose population multicalibration error, measured by Expected Calibration Error (ECE), is at most $\varepsilon$ with respect to a given family of groups. For every fixed $\kappa > 0$, in the regime $|G|\le \varepsilon^{-\kappa}$, we prove that $\widetilde{\Theta}(\varepsilon^{-3})$ samples are necessary and sufficient, up to polylogarithmic factors. The lower bound holds even for randomized predictors, and the upper bound is realized by a randomized predictor obtained via an online-to-batch reduction. This separates the sample complexity of multicalibration from that of marginal calibration, which scales as $\widetilde{\Theta}(\varepsilon^{-2})$, and shows that mean-ECE multicalibration is as difficult in the batch setting as it is in the online setting, in contrast to marginal calibration which is strictly more difficult in the online setting. In contrast we observe that for $\kappa = 0$, the sample complexity of multicalibration remains $\widetilde{\Theta}(\varepsilon^{-2})$ exhibiting a sharp threshold phenomenon. More generally, we establish matching upper and lower bounds, up to polylogarithmic factors, for a weighted $L_p$ multicalibration metric for all $1 \le p \le 2$, with optimal exponent $3/p$. We also extend the lower-bound template to a regular class of elicitable properties, and combine it with the online upper bounds of Hu et al. (2025) to obtain matching bounds for calibrating properties including expectiles and bounded-density quantiles.

cs.LG↗
arXiv2026

Multi-Objective Reinforcement Learning for Large-Scale Tote Allocation in Human-Robot Collaborative Fulfillment Centers

Optimizing the consolidation process in container-based fulfillment centers requires trading off competing objectives such as processing speed, resource usage, and space utilization while adhering to a range of real-world operational constraints. This process involves moving items between containers via a combination of human and robotic workstations to free up space for inbound inventory and increase container utilization. We formulate this problem as a large-scale Multi-Objective Reinforcement Learning (MORL) task with high-dimensional state spaces and dynamic system behavior. Our method builds on recent theoretical advances in solving constrained RL problems via best-response and no-regret dynamics in zero-sum games, enabling principled minimax policy learning. Policy evaluation on realistic warehouse simulations shows that our approach effectively trades off objectives, and we empirically observe that it learns a single policy that simultaneously satisfies all constraints, even if this is not theoretically guaranteed. We further introduce a theoretical framework to handle the problem of error cancellation, where time-averaged solutions display oscillatory behavior. This method returns a single iterate whose Lagrangian value is close to the minimax value of the game. These results demonstrate the promise of MORL in solving complex, high-impact decision-making problems in large-scale industrial systems.

cs.LG↗
arXiv2026

Model Agreement via Anchoring

Numerous lines of aim to control $\textit{model disagreement}$ -- the extent to which two machine learning models disagree in their predictions. We adopt a simple and standard notion of model disagreement in real-valued prediction problems, namely the expected squared difference in predictions between two models trained on independent samples, without any coordination of the training processes. We would like to be able to drive disagreement to zero with some natural parameter(s) of the training procedure using analyses that can be applied to existing training methodologies. We develop a simple general technique for proving bounds on independent model disagreement based on $\textit{anchoring}$ to the average of two models within the analysis. We then apply this technique to prove disagreement bounds for four commonly used machine learning algorithms: (1) stacked aggregation over an arbitrary model class (where disagreement is driven to 0 with the number of models $k$ being stacked) (2) gradient boosting (where disagreement is driven to 0 with the number of iterations $k$) (3) neural network training with architecture search (where disagreement is driven to 0 with the size $n$ of the architecture being optimized over) and (4) regression tree training over all regression trees of fixed depth (where disagreement is driven to 0 with the depth $d$ of the tree architecture). For clarity, we work out our initial bounds in the setting of one-dimensional regression with squared error loss -- but then show that all of our results generalize to multi-dimensional regression with any strongly convex loss.

cs.LG↗
arXiv2026

Prior-Agnostic Incentive-Compatible Exploration

In bandit settings, optimizing long-term regret metrics requires exploration, which corresponds to sometimes taking myopically sub-optimal actions. When a long-lived principal merely recommends actions to be executed by a sequence of different agents (as in an online recommendation platform) this provides an incentive misalignment: exploration is "worth it" for the principal but not for the agents. Prior work studies regret minimization under the constraint of Bayesian Incentive-Compatibility in a static stochastic setting with a fixed and common prior shared amongst the agents and the algorithm designer. We show that (weighted) swap regret bounds on their own suffice to cause agents to faithfully follow forecasts in an approximate Bayes Nash equilibrium, even in dynamic environments in which agents have conflicting prior beliefs and the mechanism designer has no knowledge of any agents beliefs. To obtain these bounds, it is necessary to assume that the agents have some degree of uncertainty not just about the rewards, but about their arrival time -- i.e. their relative position in the sequence of agents served by the algorithm. We instantiate our abstract bounds with concrete algorithms for guaranteeing adaptive and weighted regret in bandit settings.

cs.GT↗
arXiv2026

Personalization Aids Pluralistic Alignment Under Competition

Can competition among misaligned AI providers yield aligned outcomes for a diverse population of users, and what role does model personalization play? We study a setting where multiple competing AI providers interact with multiple users who must make downstream decisions but differ in preferences. Providers have their own objectives over users' actions and strategically deploy AI models to advance them. We model the interaction as a Stackelberg game with multiple leaders (providers) and followers (users): providers commit to conversational policies, and users choose which model to use, how to converse, and how to act. With user-specific personalization, we show that under a Weak Market Alignment condition, every equilibrium gives each user outcomes comparable to those from a perfectly aligned common model -- so personalization can induce pluralistically aligned outcomes, even when providers are self-interested. In contrast, when providers must deploy a single anonymous policy, there exist equilibria with uninformative behavior under the same condition. We then give a stronger alignment condition that guarantees each user their optimal utility in the anonymous setting.

cs.GT↗
arXiv2026

Optimal Lower Bounds for Online Multicalibration

We prove tight lower bounds for online multicalibration, establishing an information-theoretic separation from marginal calibration. In the general setting where group functions can depend on both context and the learner's predictions, we prove an $\Omega(T^{2/3})$ lower bound on expected multicalibration error using just three disjoint binary groups. This matches the upper bounds of Noarov et al. (2025) up to logarithmic factors and exceeds the $O(T^{2/3-\varepsilon})$ upper bound for marginal calibration (Dagan et al., 2025), thereby separating the two problems. We then turn to lower bounds for the more difficult case of group functions that may depend on context but not on the learner's predictions. In this case, we establish an $\widetilde{\Omega}(T^{2/3})$ lower bound for online multicalibration via an $O(\log^3 T)$-sized group family constructed from an orthonormal basis, again matching upper bounds up to logarithmic factors.

cs.LG↗
arXiv2025

Near-Optimal Dropout-Robust Sortition

Citizens' assemblies - small panels of citizens that convene to deliberate on policy issues - often face the issue of panelists dropping out at the last-minute. Without intervention, these dropouts compromise the size and representativeness of the panel, prompting the question: Without seeing the dropouts ahead of time, can we choose panelists such that after dropouts, the panel will be representative and appropriately-sized? We model this problem as a minimax game: the minimizer aims to choose a panel that minimizes the loss, i.e., the deviation of the ultimate panel from predefined representation targets. Then, an adversary defines a distribution over dropouts from which the realized dropouts are drawn. Our main contribution is an efficient loss-minimizing algorithm, which remains optimal as we vary the maximizer's power from worst case to average case. Our algorithm - which iteratively plays a projected gradient descent subroutine against an efficient algorithm for computing the best-response dropout distribution - also addresses a key open question in the area: how to manage dropouts while ensuring that each potential panelist is chosen with relatively equal probabilities. Using real-world datasets, we compare our algorithms to existing benchmarks, and we offer the first characterizations of tradeoffs between robustness, loss, and equality in this problem.

cs.GT↗
arXiv2025

Robust Decision Making with Partially Calibrated Forecasts

Calibration has emerged as a foundational goal in ``trustworthy machine learning'', in part because of its strong decision theoretic semantics. Independent of the underlying distribution, and independent of the decision maker's utility function, calibration promises that amongst all policies mapping predictions to actions, the uniformly best policy is the one that ``trusts the predictions'' and acts as if they were correct. But this is true only of \emph{fully calibrated} forecasts, which are tractable to guarantee only for very low dimensional prediction problems. For higher dimensional prediction problems (e.g. when outcomes are multiclass), weaker forms of calibration have been studied that lack these decision theoretic properties. In this paper we study how a conservative decision maker should map predictions endowed with these weaker (``partial'') calibration guarantees to actions, in a way that is robust in a minimax sense: i.e. to maximize their expected utility in the worst case over distributions consistent with the calibration guarantees. We characterize their minimax optimal decision rule via a duality argument, and show that surprisingly, ``trusting the predictions and acting accordingly'' is recovered in this minimax sense by \emph{decision calibration} (and any strictly stronger notion of calibration), a substantially weaker and more tractable condition than full calibration. For calibration guarantees that fall short of decision calibration, the minimax optimal decision rule is still efficiently computable, and we provide an empirical evaluation of a natural one that applies to any regression model solved to optimize squared error.

stat.ML↗
arXiv2025

Dynamic Regret Bounds for Online Omniprediction with Long Term Constraints

We present an algorithm guaranteeing dynamic regret bounds for online omniprediction with long term constraints. The goal in this recently introduced problem is for a learner to generate a sequence of predictions which are broadcast to a collection of downstream decision makers. Each decision maker has their own utility function, as well as a vector of constraint functions, each mapping their actions and an adversarially selected state to reward or constraint violation terms. The downstream decision makers select actions "as if" the state predictions are correct, and the goal of the learner is to produce predictions such that all downstream decision makers choose actions that give them worst-case utility guarantees while minimizing worst-case constraint violation. Within this framework, we give the first algorithm that obtains simultaneous \emph{dynamic regret} guarantees for all of the agents -- where regret for each agent is measured against a potentially changing sequence of actions across rounds of interaction, while also ensuring vanishing constraint violation for each agent. Our results do not require the agents themselves to maintain any state -- they only solve one-round constrained optimization problems defined by the prediction made at that round.

cs.LG↗
arXiv2025

Emergent Alignment via Competition

Aligning AI systems with human values remains a fundamental challenge, but does our inability to create perfectly aligned models preclude obtaining the benefits of alignment? We study a strategic setting where a human user interacts with multiple differently misaligned AI agents, none of which are individually well-aligned. Our key insight is that when the users utility lies approximately within the convex hull of the agents utilities, a condition that becomes easier to satisfy as model diversity increases, strategic competition can yield outcomes comparable to interacting with a perfectly aligned model. We model this as a multi-leader Stackelberg game, extending Bayesian persuasion to multi-round conversations between differently informed parties, and prove three results: (1) when perfect alignment would allow the user to learn her Bayes-optimal action, she can also do so in all equilibria under the convex hull condition (2) under weaker assumptions requiring only approximate utility learning, a non-strategic user employing quantal response achieves near-optimal utility in all equilibria and (3) when the user selects the best single AI after an evaluation period, equilibrium guarantees remain near-optimal without further distributional assumptions. We complement the theory with two sets of experiments.

cs.LG↗
arXiv2025

Online Omniprediction with Long-Term Constraints

We introduce and study the problem of online omniprediction with long-term constraints. At each round, a forecaster is tasked with generating predictions for an underlying (adaptively, adversarially chosen) state that are broadcast to a collection of downstream agents, who must each choose an action. Each of the downstream agents has both a utility function mapping actions and state to utilities, and a vector-valued constraint function mapping actions and states to vector-valued costs. The utility and constraint functions can arbitrarily differ across downstream agents. Their goal is to choose actions that guarantee themselves no regret while simultaneously guaranteeing that they do not cumulatively violate the constraints across time. We show how to make a single set of predictions so that each of the downstream agents can guarantee this by acting as a simple function of the predictions, guaranteeing each of them $\tilde{O}(\sqrt{T})$ regret and $O(1)$ cumulative constraint violation. We also show how to extend our guarantees to arbitrary intersecting contextually defined \emph{subsequences}, guaranteeing each agent both regret and constraint violation bounds not just marginally, but simultaneously on each subsequence, against a benchmark set of actions simultaneously tailored to each subsequence.

cs.LG↗
arXiv2025

Replicable Reinforcement Learning with Linear Function Approximation

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an algorithm produce identical outcomes when executed twice on different samples from the same distribution. Provably replicable algorithms are especially interesting for reinforcement learning (RL), where algorithms are known to be unstable in practice. While replicable algorithms exist for tabular RL settings, extending these guarantees to more practical function approximation settings has remained an open problem. In this work, we make progress by developing replicable methods for linear function approximation in RL. We first introduce two efficient algorithms for replicable random design regression and uncentered covariance estimation, each of independent interest. We then leverage these tools to provide the first provably efficient replicable RL algorithms for linear Markov decision processes in both the generative model and episodic settings. Finally, we evaluate our algorithms experimentally and show how they can inspire more consistent neural policies.

cs.LG↗
arXiv2025

Networked Information Aggregation via Machine Learning

We study a distributed learning problem in which learning agents are embedded in a directed acyclic graph (DAG). There is a fixed and arbitrary distribution over feature/label pairs, and each agent or vertex in the graph is able to directly observe only a subset of the features -- potentially a different subset for every agent. The agents learn sequentially in some order consistent with a topological sort of the DAG, committing to a model mapping observations to predictions of the real-valued label. Each agent observes the predictions of their parents in the DAG, and trains their model using both the features of the instance that they directly observe, and the predictions of their parents as additional features. We ask when this process is sufficient to achieve \emph{information aggregation}, in the sense that some agent in the DAG is able to learn a model whose error is competitive with the best model that could have been learned (in some hypothesis class) with direct access to \emph{all} features, despite the fact that no single agent in the network has such access. We give upper and lower bounds for this problem for both linear and general hypothesis classes. Our results identify the \emph{depth} of the DAG as the key parameter: information aggregation can occur over sufficiently long paths in the DAG, assuming that all of the relevant features are well represented along the path, and there are distributions over which information aggregation cannot occur even in the linear case, and even in arbitrarily large DAGs that do not have sufficient depth (such as a hub-and-spokes topology in which the spoke vertices collectively see all the features). We complement our theoretical results with a comprehensive set of experiments.

cs.LG↗