Choquet and minimax expectations are equivalent in European option pricing.
problem Pricing European options in incomplete markets.
method Comparing Choquet and minimax expectations in the context of European options.
result Choquet and minimax expectations are equal for European options.
Study apple tasting feedback in online binary classification, providing new insights into minimax expected mistakes.
problem Online binary classification with partial feedback (apple tasting).
method Combinatorial analysis, Littlestone dimension, Effective width.
result Established a trichotomy of minimax expected mistakes in the realizable setting.
MRCs minimize worst-case expected 0-1 loss and provide performance guarantees.
problem Minimizing expected 0-1 loss in classification.
method Minimizes worst-case expected 0-1 loss over uncertainty sets defined by linear constraints.
result Achieves efficient learning and generalization with performance guarantees.
We prove non-asymptotic lower bounds on the expectation of the maximum of d d d independent Gaussian variables and the expectation of the maximum of d d d independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…
Optimizes treatment allocation using covariates for better outcomes.
problem Improving treatment allocation in multi-armed bandit problems.
method Maximizes a functional of the conditional potential outcome distribution.
result Developed expected regret lower bounds and near minimax optimal policy.
Paper analyzes nonconvex bandit problems with improved adaptive methods.
problem Continuous armed bandit problems for nonconvex cost functions.
method Simple and adaptive bin splitting methods.
result Adaptive method achieves locally minimax optimal expected cumulative regret.
Optimal algorithm for identifying best-arm with minimal regret.
problem Identifying the best arm in two treatments with limited budget.
method Neyman allocation based on outcome standard deviations.
result Neyman allocation is minimax optimal for simple regret.
Study finds optimal regret bound for multi-armed bandit problem with expert advice.
problem Optimizing decision-making in a multi-armed bandit problem with expert advice.
method Proved a tight lower bound matching the upper bound of Kale (2014) for minimax expected regret.
result The minimax optimal expected regret is Θ(√(T K log (N/K))) for the problem.
Develops high-probability minimax quantile bounds for statistical problems.
problem Statistical procedures often lose information about tail behavior when reduced to expectations.
method Introduces minimax quantiles, develops high-probability variants of minimax methods, and converts risk lower bounds to quantile lower bounds.
result Obtains high-probability minimax quantile lower bounds for various statistical problems.
New algorithm for non-stationary bandits with slow drifts.
problem Minimizing dynamic regret in non-stationary bandits with slowly varying rewards.
method Extends Successive Elimination to non-stationary bandits with a novel gap profile characterization.
result First instance-dependent regret upper bound for slowly varying non-stationary bandits.
Paper explores generalization of minimax learners, proposing a new metric.
problem Understanding how minimax learners perform on unseen data.
method Proposes a new metric, the primal gap, to study generalization of minimax learners.
result Derives generalization error bounds for the primal gap in nonconvex-concave settings.
New RL algorithm minimizes distributional learning error.
problem Improving distributional reinforcement learning for better error minimization.
method Proposes a new model-based algorithm with theoretical minimax optimality.
result Proves minimax optimality for approximating return distributions.
Study optimizes best-arm identification with minimax and Bayes strategies.
problem Efficiently identifying the best arm in fixed-budget scenarios.
method Adaptive procedure with two stages: pilot phase and minimax game.
result Single strategy is asymptotically minimax and Bayes optimal.
Optimal strategy identified for minimizing regret in fixed-budget best arm selection.
problem Minimizing expected simple regret in fixed-budget best arm selection.
method Two-Stage (TS)-Hirano-Imbens-Ridder (HIR) strategy using HIR estimator.
result TS-HIR strategy is asymptotically minimax optimal.
Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.
problem Estimating discrete probability distributions under the ℓ∞ norm with improved bounds.
method Minimax bounds in expectation and high-probability tail bounds.
result Resolved open questions posed in Kontorovich and Painsky (JMLR, 2025), including a fully empirical tightest risk bound and identifying the worst-case extremal distribution.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
Paper presents an efficient algorithm for learning minimax risk classifiers with large-scale data.
problem Efficient learning of minimax risk classifiers for large-scale data with multiple classes.
method Combination of constraint and column generation for efficient learning.
result 10x speedup for general large-scale data and 100x speedup with many classes.
Exact minimax risk derived for linear prediction with sample covariance analysis.
problem Understanding the minimax risk in linear prediction under various covariate distributions.
method Exact minimax risk analysis, leveraging statistical leverage scores and PAC-Bayes techniques.
result The minimax risk is of order d / ( n − d + 1 ) d/(n-d+1) d / ( n − d + 1 ) for any covariate distribution, nearly matching the risk for Gaussian design. AEW estimator achieves optimal risk in expectation for large enough temperatures.
problem Understanding minimax-rate optimality of AEW estimator in model selection aggregation.
method Analyzing AEW estimator with exponential weights for squared loss under random design.
result AEW achieves excess risk T log ( M ) / ( n + 1 ) T \log (M) / (n+1) T log ( M ) / ( n + 1 ) in expectation for large enough temperatures. Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss and receives a feedback signal, both of which are fixed functions of the action a…
Double Machine Learning estimators are asymptotically inadmissible under structure-agnostic models.
problem Minimax estimators may be inadmissible under structure-agnostic models.
method Exhibit second-order (U-statistic) estimators that asymptotically dominate DML estimators.
result Double Machine Learning estimators are asymptotically inadmissible under structure-agnostic models.
Given a task of predicting Y Y Y from X X X , a loss function L L L , and a set of probability distributions Γ Γ Γ on ( X , Y ) (X,Y) ( X , Y ) , what is the optimal decision rule minimizing the worst-case expected loss over Γ Γ Γ ? In this paper, we address this question by introducing a generalization of the principle of maximum entropy. Applying t…
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
GAT-GMM improves GANs' performance in learning Gaussian mixture models.
problem GANs struggle with multi-modal distributions like Gaussian mixtures.
method Proposes a minimax GAN framework using random linear generator and softmax-based quadratic discriminator.
result Gradient Descent Ascent method converges to an approximate minimax point.
Paper reconciles minimax rates and optimal recovery rates for noisy observations.
problem Estimating a function from noisy observations.
method Develops NLA minimax rates for Besov classes in L q L_q L q -norms. result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
New algorithm tackles multiclass transductive online learning with unbounded labels.
problem Characterizing optimal mistake bound for unbounded label spaces.
method Introducing new combinatorial dimensions (Level-constrained Littlestone and Branching dimensions) to characterize online learnability.
result Established trichotomy of possible minimax rates for unbounded label spaces: Θ ( T ) Θ(T) Θ ( T ) , Θ ( log T ) Θ(\log T) Θ ( log T ) , or Θ ( 1 ) Θ(1) Θ ( 1 ) . Diffusion models achieve nearly optimal distribution estimation in various spaces.
problem Theoretical limitations of diffusion modeling for distribution estimation.
method Analysis of approximation and generalization abilities of diffusion models in Besov spaces.
result Diffusion models achieve nearly minimax optimal estimation rates in total variation and Wasserstein distances.
Study tests uniformity of categorical data against missing-ball alternatives, finding chi-squared test outperforms.
problem Testing uniformity of categorical data against missing-ball alternatives.
method Characterizes minimax risk, uses collisions and chi-squared test, reduces to structured subset of alternatives.
result Minimax test outperforms chi-squared test under least favorable alternative.
We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over jo…
Study minimax regret in bilateral trade with heavy-tailed valuations.
problem Minimizing regret in bilateral trade with infinite variance valuations.
method Extended self-bounding property, truncated-mean estimation, epoch-based algorithm.
result Achieves regret bound of O ( T 1 − 2 β ( p − 1 ) / ( β p + d ( p − 1 ) ) ) O(T^{1-2β(p-1)/(βp + d(p-1))}) O ( T 1 − 2 β ( p − 1 ) / ( β p + d ( p − 1 )) ) under specific conditions. This work optimizes identifying good arms in nonparametric multi-armed bandits.
problem Efficiently identifying arms with high means in nonparametric settings.
method Combining reward-maximizing sampling with a nonparametric sequential test for anytime-valid labeling.
result Achieves minimax optimal stopping times for identifying arms above a threshold.
Paper introduces MRCs that minimize worst-case 0-1 loss, providing tight performance guarantees.
problem Minimizing worst-case 0-1 loss in classification.
method MRCs that minimize worst-case 0-1 loss with uncertainty sets of distributions.
result MRCs provide tight performance guarantees and are strongly universally consistent.
Bayesian deconditioning improves downscaling of spatial fields.
problem Challenges in refining low-resolution spatial fields with high-resolution information.
method Proposes a Bayesian formulation of deconditioning to solve the inverse problem of conditional expectation.
result Shows substantial improvements in atmospheric field downscaling over existing methods.
New algorithm reduces bandit regret to log^3(T).
problem Noise model for linear stochastic bandits with vanishing noise.
method Weighted least-squares estimation, leveraging eigenvalue relation.
result Minimax regret scaling as log^3(T) for time horizon T.
UCBVI-γ algorithm minimizes regret in discounted MDPs.
problem Minimizing regret in discounted MDPs.
method Optimism in the face of uncertainty principle and Bernstein-type bonus.
result UCBVI-γ achieves nearly minimax optimal regret.
We study the linear contextual bandit problem with finite action sets. When the problem dimension is d d d , the time horizon is T T T , and there are n ≤ 2 d / 2 n \leq 2^{d/2} n ≤ 2 d /2 candidate actions per time period, we (1) show that the minimax expected regret is Ω ( d T ( log T ) ( log n ) ) Ω(\sqrt{dT (\log T) (\log n)}) Ω ( d T ( log T ) ( log n ) ) for every algorithm, and (2) introduce a V…
In treatment allocation problems the individuals to be treated often arrive sequentially. We study a problem in which the policy maker is not only interested in the expected cumulative welfare but is also concerned about the uncertainty/risk of the treatment outcomes. At the outset, the total number of treatment assign…
This paper analyzes neural networks for solving complex optimization problems.
problem Minimax optimization problems in infinite-dimensional function spaces.
method Mean-field analysis of stochastic gradient descent-ascent in neural networks.
result The algorithm converges to a stationary point at a sublinear rate.
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our main contributions come in the form of minimax lower bounds for the expected pe…
Wasserstein framework solves mixed linear regression problems.
problem Mixed linear regression with multi-modal distributions.
method Wasserstein distance minimization for nonconvex-concave minimax optimization.
result WMLR achieves global convergence and generalization guarantees for two linear models.
The paper tackles optimal policy learning with asymmetric counterfactual utilities in healthcare decisions.
problem Learning optimal policies from observed data with asymmetric counterfactual utilities.
method The approach involves identifying and minimizing the maximum expected utility loss using statistical decision theory and solving intermediate classification problems.
result One can learn minimax loss decision rules from observed data.
Optimal adaptive experiment for choosing best treatment with binary outcomes.
problem Choosing the best treatment from binary options in an adaptive experiment.
method Adaptive experiment with two phases: treatment allocation and choice. Neyman allocation method used.
result Neyman allocation is minimax and Bayes optimal, matching lower bounds for regret.
We describe a novel extension of soft actor-critics for hierarchical Deep Q-Networks (HDQN) architectures using mutual information metric. The proposed extension provides a suitable framework for encouraging explorations in such hierarchical networks. A natural utilization of this framework is an adversarial setting, w…
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
New methods tackle statistical inverse problems with random data.
problem Statistical inverse problems with random experimental design.
method Spectral regularization, regularization by projection, convex penalties.
result Minimax rates in expectation and probability for convergence.
T-Cal tests model calibration with a minimax optimal test.
problem Detecting mis-calibration of predictive models using a finite validation dataset.
method T-Cal is a minimax optimal test for calibration based on a debiased plug-in estimator of the ℓ 2 \ell_2 ℓ 2 -Expected Calibration Error (ECE). result T-Cal is a practical tool for testing the calibration of probabilistic classification methods.
The paper addresses decision making with partially calibrated forecasts, offering a robust approach.
problem Developing a decision-making strategy for forecasts that are only partially calibrated.
method A minimax approach to mapping predictions to actions, considering worst-case distributions.
result The minimax optimal decision rule is to trust predictions and act accordingly, even for partially calibrated forecasts.
Paper presents IMRCs for evolving tasks with forward and backward learning.
problem Incremental learning of evolving tasks with few samples per task.
method Incremental minimax risk classifiers (IMRCs) that exploit forward and backward learning.
result IMRCs provide significant performance improvement, especially with reduced sample sizes.