Plan Regret

Follow this topic Ask about this topic

Momentum

2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Jul 6Week of Sep 21

Latest papers 17

Sep 28, 2026cs.CY

Beyond Energy: When Sustainability Dimensions Reshape LLM Serving Decisions

Large language model (LLM) serving has environmental impacts across energy consumption, carbon emission, water consumption, and biodiversity loss. Yet these dimensions are largely evaluated in isolation, leaving it unclear when and how they lead to different optimization decisions. We present PRISM, a unified framework for characterizing and optimizing LLM serving across energy, carbon, water, and biodiversity impacts. Our analysis reveals a fundamental distinction: computing configurations determine energy consumption, whereas where and when LLM serving is deployed determine its carbon, water, and biodiversity impacts. Under a fixed deployment choice and operational-only accounting, all dimensions preserve the same energy-based configuration ranking. Deployment rankings can diverge across dimensions, while embodied impacts can break configuration invariance when they exceed a lifecycle crossover boundary. PRISM identifies these conditions, quantifies cross-dimensional regrets, and balances the four dimensions. In regional-routing experiments, PRISM reduces median worst-case regret by 50.2% relative to the strongest baseline.

Tianyao Shi, Xipeng Shen, Yi Ding

Elmore Family School of Electrical and Computer Engineering, Purdue University, USA

Large Language Model Serving Energy Consumption Energy Resources Energy-Efficient Decisions Prism+1

Sep 7, 2026cs.LG

Guiding Worker Self-Selection in Crowdsourcing Contests: An LLM-Augmented Algorithmic Approach

Crowdsourcing platforms coordinate large pools of online workers who strategically choose which contests to enter and how much effort to invest. This self-selection can leave important contests with too few participants or too little effort, while workers may regret entering contests that leave them worse off than available alternatives. We study how platforms can recommend contests to workers using self-selection in Tullock contests (SSTC), a two-stage model in which workers first choose contests and then compete within them. We introduce GRAF, a greedy polynomial-time framework that constructs self-selection outcomes by ordering workers according to a score vector, with guarantees of zero worker regret and platform optimality in special cases of SSTC. Because effective orderings are difficult to design under worker heterogeneity, we propose LLMScore, an LLM-driven evolutionary framework that automatically designs GRAF's scoring algorithm. LLMScore addresses two challenges: jointly optimizing platform utility and worker satisfaction, and evaluating worker regret when exact computation is intractable. Trained only on small instances of one setting, it transfers to larger and structurally different settings; moreover, its output is human-readable code that platform operators can inspect and modify. Across 1,000 synthetic instances spanning four settings, GRAF with LLMScore consistently achieves high-quality, often near-optimal, outcomes with low worker regret, benefiting both platforms and workers.

Nguyen Thach, Hau Chan, David Parkes +1

University of Nebraska-Lincoln Lincoln, Nebraska, USA · Harvard University Cambridge, Massachusetts, USA

Crowdsourced Framework Competition Selection Bias Plan Regret Optimality

Aug 31, 2026cs.LG

Constant Individual Regret in General Games

Uncoupled no-regret dynamics provide a decentralized route to equilibrium, but prior guarantees for individual regret retain a polylogarithmic dependence on the horizon. We remove this dependence for every finite

N

-player normal-form game under full-information feedback. We introduce \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average. The algorithm is deterministic and fully uncoupled. If

m_{\max}

denotes the largest action-set size, then, simultaneously for every horizon

T\geq1

, it guarantees that each of the

N

players in the game incurs regret upper bounded by

O(\textrm{poly}(N, \log m_{\max}))

. Our algorithm leverages a new form of optimism inspired by modern filter design.

Mingyang Liu, Gabriele Farina, Asuman Ozdaglar

LIDS, EECS, Massachusetts Institute of Technology

Imperfect-Information Games Plan Regret Optimistic Follow-The-Regularized-Leader Exponential Moving Average

Jul 27, 2026cs.LG

Generative Distributionally Robust Optimization

Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data. We propose Generative Distributionally Robust Optimization (GDRO), a principled framework that accepts any sampleable conditional generator as the nominal model and restricts worst-case laws to a chosen conditional generator family. The key is the sampler-Sinkhorn pairing: samplers represent the conditional laws exactly, while Sinkhorn divergence compares their induced distributions without likelihood access and can be estimated from samples alone. The resulting population problem admits a direct finite-sample approximation and differentiable primal-dual implementation at the active decision context. For Lipschitz losses, the population Sinkhorn radius bounds downstream degradation. Across explicit and implicit generators, our method reduces rare-context inventory regret by 60% and SocialGAN navigation collisions by 50% relative to nominal decisions.

Ziwei Zhang, Jonathan Yu-Meng Li, Zhihao Jin

1Telfer School of Management, University of Ottawa · Department of Electrical and Computer Engineering, Western University

Distributionally-Robust Optimization Robust Optimization Distributions Generative Models Primal-Dual Methods Bounded Adversary+1

Jul 26, 2026cs.LG

Short-Term Pain for Long-Term Gain: Adaptive Experiment with Post-Commitment Reward Shift

Decision-makers in learning environments face a dilemma when their short-term optimal actions may not favor their long-term benefits the most. To understand the fundamental tradeoff behind the dilemma, we study adaptive experimentation with post-commitment reward shifts. During an experiment phase, the decision-maker may adaptively test multiple options; during a subsequent commitment phase, the decision-maker must commit to a single option, whose reward may differ from its pre-commitment reward. We propose the Reserved Arm Eliminations for Commitment (RAEC) algorithm, which reserves a predetermined portion of the experiment phase to identify the best post-shift option while using the remaining rounds to minimize short-run regret. We establish regret upper bounds for RAEC across all parameter regimes and matching minimax lower bounds, providing a tight characterization of the cost of balancing short-term performance and long-term commitment. We also study two extensions. With prior structural knowledge linking pre- and post-shift rewards, we show that correctly identifying the ranking-changing component of the shift is more important than estimating its absolute magnitude. For settings with concave commitment rewards and portfolio choice, we develop the Reserved Online Stochastic Convex Optimization for Commitment (ROSCOC) algorithm, which directly converts its reserved exploration history into a commitment portfolio and achieves tight regret bound. Finally, we also conduct numerical experiments which confirm that our proposed algorithms achieve the desired regret predicted by our theory, and also outperform other baseline algorithms.

Puping Jiang, Wei Tang

Antai College of Economics and Management, Shanghai Jiao Tong University · The Chinese University of Hong Kong

Plan Regret Stochastic Convex Optimization Long-Term

Jul 25, 2026cs.LG

Training with (Swap) Regret Loss in a Single-Layer Self-Attention Model: A Case Study on the Probability Simplex

We revisit the regret loss framework introduced in Park et al. (2025), which uses decision-theoretic regret as a direct loss function for training models to make better decisions, through the lens of probability-simplex policies. Our first result shows that a single-layer self-attention model trained with regret loss admits a stationary point whose forward-pass exactly matches smoothed fictitious play with the appropriate stepsize that ensures no-regret behavior-i.e., for any given policy input, the model outputs the same update that smoothed fictitious play would produce. In parallel, we also newly introduce a swap-regret loss function, which extends the regret-loss framework beyond external regret and enables models to directly optimize for swap-deviation robustness. We further show that this swap-regret loss admits a stationary point whose forward pass implements the corresponding swap-regret update induced by classical Blum-Mansour no-pass implementation algorithm, with each head implementing an external-regret update via smoothed fictitious play. Together, these results show that regret-trained attention can realize differentiable mechanisms whose deployment induces equilibrium behavior in games: external-regret dynamics lead to coarse correlated equilibrium, while swap-regret dynamics lead to correlated equilibrium. Thus, regret-based objectives steer minimal attention architectures toward online-learning dynamics with game-theoretic guarantees, without supervised traces of those algorithms.

Chanwoo Park, Asuman Ozdaglar

1MIT EECS

Plan Regret Self-Play Minimax Rate Switch Probability

Jul 23, 2026cs.CL

One More Turn, Less Regret: A Regret-Based Multi-Turn Benchmark for LLMs' Clarification Policies

Ambiguous user requests make clarification a sequential decision problem for conversational LLM assistants: they must decide whether to ask, what to ask, when to stop, and when to answer. We introduce RegretBench, a multi-turn benchmark that evaluates clarification as policy behavior rather than isolated question quality. RegretBench provides a hidden-intent formulation of ambiguity, supports free-form interaction grounded in semantic-state tracking, and introduces a regret-based objective that measures how much value a model loses relative to a reference clarification policy. Experiments on open-domain QA and product recommendation scenarios show that final success alone is insufficient, as models with similar accuracy can differ substantially in efficiency, robustness to user behaviors, and stopping decisions. By jointly measuring intent resolution, interaction cost, ineffective clarification, and regret, RegretBench reveals whether models clarify usefully and efficiently. Our results show that effective clarification requires more than plausible questions: models must ask the right question at the right time and stop once the user's intended meaning is clear.

Minh Ngoc Ta, My Anh Tran Nguyen, Duong D. Nguyen +2

MBZUAI · BKAI Research Center, Hanoi University of Science and Technology · INSAIT, Sofia University "St. Kliment Ohridski"

Clarification Question Multi-Turn Benchmark Plan Regret Regret

Jul 21, 2026math.OC

Online Optimization of Difference-of-Convex Compositions with Smooth Mappings

We study online optimization for a broad class of structured non-convex non-smooth problems where each loss is a composition of a difference-of-convex function with a smooth mapping, and the feasible region is defined by constraint functions of the same kind. We propose a time-smoothed proximal linear algorithm and a local-regret measure based on a proximal residual mapping. We show that this residual is a proper stationarity measure for the original problem: its fixed-point condition implies first-order stationarity. Our analysis relies on a tangent-cone characterization for a feasible region described by composite difference-of-convex constraints, which is of independent interest and allows each update to be computed via a convex optimization oracle, despite the non-convexity of the problem. We establish a local-regret bound and a bound on the total number of inner convex subproblems. We also derive an error bound connecting the proximal residual to the distance to stationarity, providing a quantitative certificate of approximate stationarity.

Jingwei Ji, Jong-Shi Pang, Renyuan Xu

Management Science and Engineering, Stanford University · The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California

Stochastic Convex Optimization Plan Regret

Jul 20, 2026cs.LG

Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles

Stochastic nonconvex optimization is central to training deep networks and LLMs in modern machine learning. We give a black-box reduction from stochastic nonconvex optimization to ordinary static regret minimization in online convex optimization (OCO), thereby resolving the open problem posed by Chen and Hazan (2024). Our reduction maintains a predictable gradient tracker, while a black-box online learner

\mathcal{A}

selects a preconditioner that transforms this tracker into the update direction. Given a

β

-smooth function with a range bounded by

M

and an unbiased gradient oracle with variance bounded by

σ^2

, we bound the expected average squared gradient norm by

O(σ\sqrt{Mβ/T}+\sqrt{Mβ}\mathrm{Reg}_T(\mathcal{A})/T+\frac{Mβ}{T})

, where

\mathrm{Reg}_T(\mathcal{A})

is the static regret of

\mathcal{A}

. Thus, any OCO oracle with

O(\sqrt{T})

regret recovers the classical

O(T^{-1/2})

convergence rate. We further extend the framework to nonsmooth nonconvex objectives, still relying only on ordinary static regret, and attain the optimal convergence rate for Goldstein-type stationarity. Finally, we conduct numerical experiments on nonconvex objectives to illustrate how the reduction exploits online-selected preconditioners while using the same stochastic-oracle budget as stochastic gradient descent.

Haichen Hu, David Simchi-Levi

Center for Computational Science and Engineering, MIT · Department of Civil and Environmental Engineering, MIT · Institute for Data, Systems, and Society, MIT

Stochastic Convex Optimization Interval Regret Plan Regret Lipschitz Continuity Preconditioner Black Box

Jul 12, 2026cs.LG

Lower Bound on the Cumulative Constrained Violation for the OGD+Projection algorithm for Constrained Online Convex Optimization (COCO)

The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action

x_t \in \mathcal{X} \subset \mathbb{R}^d

, a convex loss function

f_t

and a convex constraint function

g_t

that drives the constraint

g_t(x)\le 0

are revealed. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV) compared to the benchmark that knows the loss functions and constraint functions

f_t

and

g_t

for all

t

ahead of time, and chooses a static optimal action that is feasible with respect to all

g_t(x)\le 0

. Currently, the best known algorithm is OGD+Projection algorithm of [Vaze and Sinha, 2025] that has simultaneous regret of

O(\sqrt{T})

and CCV of

O(T^{1/3})

for

d=2

[Balasundaram et al., 2026], and simultaneous regret of

O(\sqrt{T})

and CCV of

O(\sqrt{T})

for any

d

[Sarkar and Sinha, 2026]. In this paper, we show that the CCV of the OGD+Projection algorithm is

Ω(T^{\frac{d-1}{2d}})

. This is the first such lower bound result.

Haricharan Balasundaram, Karthick Krishna Mahendran, Rahul Vaze

\Widetilde{\Mathcal{O}}(\Sqrt{T})$ Regret Convex Loss Plan Regret Lower Bounds Structural Constraints

Jun 18, 2026math.OC

Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning

We introduce optimal coarse correlated equilibria for continuous-time mean field games. A coarse correlated equilibrium is a randomized recommendation scheme from which no player can gain by ignoring the recommendation and switching to an alternative strategy. The problem is as follows: a moderator selects, among all mean-field coarse correlated equilibria, one that optimizes a prescribed performance criterion, which may differ from the representative player's objective. After formulating the problem, we develop a linear programming (LP) formulation, prove the existence of optimal LP coarse correlated equilibria, and relate the LP characterization to the original probabilistic setting. Building on this characterization, we design a no-regret primal-dual algorithm, based on an equivalent Lagrangian formulation of the external-regret constraint, for learning such equilibria. We provide explicit convergence rates for the learning algorithm, and numerical examples illustrate the method.

Luciano Campi, Federico Cannerozzi, Ioannis Tzouanas

DEPARTMENT OF MATHEMATICS “FEDERIGO ENRIQUES”, UNIVERSITY OF MILAN, VIA SALDINI 50, 20133, MILAN, ITALY. · CENTER FOR MATHEMATICAL ECONOMICS (IMW), BIELEFELD UNIVERSITY, BIELEFELD, GERMANY.

Mean Field Games Equilibrium Mean-Field Limit Plan Regret Linear Programming Recommendation Quality

Jun 15, 2026cs.LG

Filtered ANN as a Phase Transition: When Selectivity-Estimation Error Causes Plan Regret

A filtered approximate-nearest-neighbor (ANN) query returns the k nearest vectors among those satisfying an attribute predicate P of selectivity s. The best execution strategy -- pre-filter, post-filter, or in-filter -- changes with s, so a system must estimate s and choose. We model this as an argmax over a landscape with phases (regions where each strategy wins) separated by boundaries, and show that selectivity-estimation error produces plan regret -- recall lost versus the oracle strategy -- only in the critical regions around those boundaries. The regret is a wedge of log-width equal to the multiplicative estimation error epsilon and height equal to the local cliff |V'(s*)| epsilon; the flip-margin 1/|V'(s*)| is the condition number of a sibling cardinality-estimation study reappearing as the local boundary theory. The two phase boundaries follow from independent mathematics: order statistics place the post-filter cliff at s ~ k/K, and site percolation places the in-filter cliff at s_c ~ 0.83/M for graph degree M (corpus-size independent). Criticality exists only under a constrained budget B < sqrt(k n). Under pre-registered decision rules we confirm, on synthetic sweeps and real SIFT1M, that regret concentrates ~290x at the boundary and that the regret curves obey a finite-size scaling collapse onto one universal wedge across two decades of corpus size. A real approximate index does not mis-locate the boundary, but a biased cost model opens a persistent miscalibration band that estimation-error robustness cannot fix. The contribution is a characterization, not a new index. Code and the full pre-registration are public.

Madhulatha Mandarapu, Sandeep Kunkunuru

VaidhyaMegha Private Limited, India

Approximate Nearest-Neighbor Search Plan Regret Selectivity Regret Approximation Cardinality+2

Jun 14, 2026cs.DB

When Does q-error Predict Plan Regret? Three Regimes of Cardinality-Estimation Error

Cardinality-estimation (CE) research ranks estimators by q-error, yet it is well known that q-error is an imperfect proxy for query-plan quality. We give a measurement-driven account of when it is a good proxy and when it is not, and why. Modeling plan selection as an argmin over a piecewise-linear cost landscape, we find that plan regret (the cost of the chosen plan relative to the optimal, under true cardinalities) is governed by plan-cost geometry in a regime-dependent way. (i) For small errors, a true-point condition number kappa predicts regret and out-predicts q-error; its predictive power decays to zero as error grows, as a local linearization must. (ii) For large errors -- where deployed learned estimators operate -- an estimator-independent average-case sub-optimality measure ACS-infinity predicts which queries are regret-prone (Spearman rho ~ 0.54 on STATS-CEB), while q-error is nearly uninformative at the query level (rho ~ 0.05). (iii) The worst case is Haritsa's maximum sub-optimality (MSO). The three are one cost-ratio spectrum under three weightings. We prove a limit law ACS-infinity = sum_k r_k pi_k with cardinality-independent combinatorial weights, and validate every claim on STATS-CEB and JOB-light with four released estimators under pre-registered decision rules, and confirm on real PostgreSQL runtime that ACS-infinity predicts regret where q-error does not. The contribution is conceptual and empirical -- an average-case companion to worst-case robust query optimization, and a characterization of when an accuracy metric tracks plan quality -- rather than a new estimator. Code and the full pre-registration are public.

Madhulatha Mandarapu, Sandeep Kunkunuru

VaidhyaMegha Private Limited, India

Prediction Error Plan Regret Regret Combinations

May 31, 2026cs.LG

Fairness in two-player zero-sum games with bandit feedback

We study two-player zero-sum games (TPZSGs) with bandit feedback under fairness constraints requiring every action to be played with probability at least

α/m

. Existing instance-dependent results target

\textit{pure}

Nash equilibria, while fairness generically produces

\textit{mixed}

equilibria, a harder learning target. Our key technical tool is a reparametrization: every fair strategy decomposes as

p = (α/m)\mathbf{1} + (1-α)\widetilde{p}

with

\widetilde{p} \in Δ_m

, and substituting into the payoff form yields

p^{\top}Aq = \widetilde{p}^{\top}\widetilde{A} q

for a fair payoff matrix

\widetilde{A} := (1-α)A + α\mathbf{1} c^{\top}

, where

c_j = \tfrac{1}{m}\sum_i A(i,j)

is the column-mean vector. The fair game on

A

is then equivalent to a standard zero-sum game on

\widetilde{A}

, so equilibrium existence, KKT structure, and LP basis stability reduce to classical results applied to

\widetilde{A}

. We derive the fair minimax value, fair Nash equilibrium, fair regret, and a clean dual representation showing the price of fairness is at most

α(1-1/m)

and vanishes whenever the unconstrained equilibrium already has full support. Our main result is an

\widetilde{O}(T^{2/3})

regret bound for an Explore-Then-Commit algorithm,

\texttt{Fair-ETC-TPZSG}

, applicable to general mixed fair equilibria, together with a discussion of why naive action elimination does not readily improve it. When the fair equilibrium has a single dominant action, equivalently when

\widetilde{p}^{\star}

is a vertex of

Δ_m

, the bound sharpens to instance-dependent

\widetilde{O}(1/\widetildeΔ(α)^{2})

, where

\widetildeΔ(α)

is the LP-margin gap.

S Akash, Pratik Gajane

LatentForce.ai Bengaluru, India · Laboratoire d’Informatique Fondamentale d’Orléans University of Orléans, France

Imperfect-Information Games Bandits Equilibrium Algorithmic Fairness Plan Regret Feedback

May 15, 2026cs.LG

Boundedly Rational Meta-Learning in Sequential Consumer Choice

Many consumer decisions are repeated choices under uncertainty. Standard models capture these decisions using Bayesian learning and dynamic programming: consumers update beliefs from feedback and use those beliefs to guide future choices. In many markets, however, learning does not restart when consumers enter a new context: prior experience with a brand, product, or provider can shape beliefs in later, related decisions. We study this cross-context knowledge transfer, or meta-learning, in sequential choice. We design a hierarchical laboratory task in which participants repeatedly choose among airlines across routes and observe noisy binary outcomes. Reduced-form evidence shows that participants improve not only within routes, but also across routes: they choose better airlines earlier in later routes and reduce pseudo-regret. To identify the mechanism behind this transfer, we compare human choices to a no-transfer benchmark and a fully integrated Bayesian meta-learning benchmark. In particular, we introduce a class of boundedly rational meta dynamic programming policies, BRMDP(D), that approximate full integration using a limited number of hyper-posterior draws, denoted by D. Trial-by-trial likelihood comparisons show that low-D boundedly rational meta-learning, especially BRMDP(1), fits participant behavior better than both no transfer and fully integrated Bayesian transfer. Consumers, therefore, transfer brand-level regularities across contexts, but through coarse representations of prior uncertainty. The findings imply that models of consumer learning should allow for approximate cross-context transfer, and that managerial counterfactuals based on either no-transfer or fully integrated learning can be misleading.

Mehrzad Khosravi, Max Kleiman-Weiner, Hema Yoganarasimhan

University of Washington

Meta-Learning Consumption Plan Regret Choice

May 11, 2026stat.ML

Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.

Masaki Adachi, Anita Yang, Yakun Wang +1

Toyota Motor Corporation · Lattice Lab · University of Bristol

Black-Box Optimization Diffusion Models Plan Regret Regret Convergence

May 2, 2026cs.LG

Decision-Focused Learning via Tangent-Space Projection of Prediction Error

Decision-Focused Learning (DFL) trains predictors to improve downstream decision quality, but computing regret gradients typically requires differentiating through solvers or relying on surrogate losses, which can be computationally expensive or deviate from the true objective. We show that, under standard regularity with locally stable active constraints, the regret gradient admits a closed-form geometric characterization, equivalent to the prediction error projected onto the tangent space of active constraints, scaled by local curvature. This reveals that regret gradients can be obtained by filtering decision-irrelevant components from the MSE gradient, providing a simpler and more direct alternative to existing approaches. Based on this, we propose PEAR (Projected Error As Regret-gradient), which computes regret gradients via a reduced linear system over active constraints, avoiding differentiation through solver iterations or additional optimization solves. Experiments on LP benchmarks and a real-world QP task show that PEAR achieves the best decision quality among all baselines while being the most computationally efficient, with gains that persist under constraint shifts.

Junhyeong Lee, Sangjin Jin, Yongjae Lee

Department of Industrial Engineering, Ulsan National Institute of Science and Technology, Ulsan, South Korea.

Plan Regret Prediction Error Structural Constraints Solver Iterations