Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.35004

Follow the Regularized Leader Does Not Converge in Constrained Optimization

Ioannis Anagnostides·Ioannis Panageas·Nikolas Patris·Tuomas Sandholm
View original source ↗Read source document ↗Export metadata ↓

Abstract

Follow the regularized leader (FTRL) is a foundational algorithm in online learning whose regret properties have been extensively studied for decades. However, in stark contrast to mirror descent---and gradient descent in particular---the convergence of FTRL to first-order stationary points in constrained nonconvex optimization was not well understood. In this paper, we show that continuous-time FTRL can fail to converge even asymptotically in infinitely smooth constrained optimization problems: its Karush-Kuhn-Tucker (KKT) gap can remain bounded away from zero indefinitely. This is especially surprising in light of the fact that continuous-time FTRL guarantees a monotonic improvement of the objective value. As a result, we establish that non-convergent behavior of no-regret dynamics---which besets general variational inequality problems---can occur even in potential systems. From a technical standpoint, our construction relies on an infinitely differentiable function where the gradient flow dynamics exhibit decelerating oscillations without ever converging pointwise, which we in turn embed into higher-dimensional FTRL dynamics that sustain a perpetually large KKT gap. We complement our negative result by showing that FTRL with Euclidean regularization does converge when the objective function is analytic. This shows that the analytic property plays a more fundamental role for FTRL than for gradient flow: it governs not only pointwise convergence, but convergence to first-order stationarity itself.

Explore related subjects

cs.GTmath.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ioannis Anagnostides, Ioannis Panageas, Nikolas Patris, Tuomas Sandholm. 2026-10-26. Follow the Regularized Leader Does Not Converge in Constrained Optimization. https://arxiv.org/abs/2610.35004

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Nash Incentive-compatible Online Mechanism Learning via Weakly Differentially Private Online Learning

We study a multi-round mechanism design problem, where we interact with a set of agents over a sequence of rounds. We wish to design an incentive-compatible (IC) online learning scheme to maximize an application-specific objective within a given class of mechanisms, without prior knowledge of the agents' type distributions. Even if each mechanism in this class is IC in a single round, if an algorithm naively chooses from this class on each round, the entire learning process may not be IC against non-myopic buyers who appear over multiple rounds. On each round, our method randomly chooses between the recommendation of a weakly differentially private online learning algorithm (e.g., Hedge), and a commitment mechanism which penalizes non-truthful behavior. Our method is IC and achieves $O(T^{\frac{1+h}{2}})$ regret for the application-specific objective in an adversarial setting, where $h$ quantifies the long-sightedness of the agents. When compared to prior work, our approach is conceptually simpler,it applies to general mechanism design problems (beyond auctions), and its regret scales gracefully with the size of the mechanism class.

cs.GT↗
arXiv2026

Rethinking Data Value: Asymmetric Data Shapley for Structure-Aware Valuation in AI Model Markets

Modern AI model markets assemble models from heterogeneous pipeline contributions, including raw data, derivative data, and data-related services, whose value can depend on upstream inputs and inherited model states. Conventional valuation approaches focus on data contributions without explicitly accounting for these production relationships. They can therefore misattribute value by evaluating contributions outside their upstream production context. We formalize this pipeline-context valuation mismatch and develop Asymmetric Data Shapley (ADS), a unified framework for structure-aware value attribution. ADS translates documented production relationships into ordered valuation groups and evaluates contributions among peers conditional on their upstream production context. We provide an axiomatic characterization of the resulting allocation and quantify allocation uncertainty when evidence supports multiple valuation structures. To support valuation at larger scales or with costly utility evaluations, we develop a Monte Carlo estimator (MC-ADS) and a surrogate-assisted estimator (SA-MC-ADS). Experiments show that ignoring production dependencies systematically shifts value toward redundant derivative data and away from useful upstream data and services. Moreover, experiments on derivative data selection and on dataset procurement during multi-stage large language model fine-tuning show that decisions guided by ADS improve downstream model performance relative to the respective benchmarks.

cs.GT↗
arXiv2026

Compliance Moral Hazard and the Backfiring Mandate

Competing firms that share a population of risky customers face a decentralized risk detection problem in which each firm holds fragmentary information whose aggregation would generate social value, but private incentives impede truthful sharing. We develop a dynamic mechanism design framework for this setting and identify three strategic frictions that distinguish it from classical mechanism design with decentralized information: compliance moral hazard, adversarial adaptation, and information destruction through intervention. A temporal value assignment (TVA) mechanism credits firms using a strictly proper scoring rule applied to discounted verified outcomes; under stated assumptions, TVA implements truthful posterior reporting as a Bayes--Nash equilibrium (uniquely optimal at each edge in large federations, with $O(1/m)$ shading in finite systems). A network Shapley characterization shows that under edge-additive coalition value, each firm's marginal contribution is proportional to its weighted cross-firm interaction degree, yielding a sharp prescription for coalition design that prioritizes inter-firm volume over firm size. Embedding TVA in a model of competition among firms, we establish a welfare ordering across four regulatory regimes (autarky, voluntary federation, mandated full sharing, TVA) and identify conditions under which information-sharing mandates without compatible incentive design reduce welfare below autarky: a ``backfiring mandate.'' We illustrate the framework on a 1.4M-transaction synthetic anti-money-laundering benchmark; the same machinery extends to platform fraud, cybersecurity threat intelligence, and supply chain risk detection.

cs.GT↗