Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is tempting to apply gradient descent to solve minimax optimization given its popularity a…
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48 results for “sequential minimax optimization”
New method for sequential probability assignment reduces regret using contextual Shtarkov sums.
problem Minimizing regret in sequential probability assignment with arbitrary hypothesis classes.
method Introducing contextual Shtarkov sum and contextual Normalized Maximum Likelihood (cNML) algorithm.
result The contextual Shtarkov sum characterizes minimax regret and provides a minimax optimal strategy.
Paper proposes SMO for solving bilevel optimization problems efficiently.
problem Solving bilevel optimization problems with nonsmooth convex lower-level and nonconvex upper-level objectives.
method Sequential minimax optimization (SMO) method using modified augmented Lagrangian and penalty schemes.
result Improves operation complexity for finding -KKT solutions.
New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
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.
Study on optimal rates for sequential probability assignment using smoothed analysis.
problem Optimal rates for sequential probability assignment under smoothed adversaries.
method General-purpose reduction from minimax rates to transductive learning, development of an efficient algorithm using MLE oracle.
result Optimal (logarithmic) fast rates for parametric and finite VC dimension classes, sublinear regret for general classes.
We consider the sequential anomaly detection problem in the one-class setting when only the anomalous sequences are available and propose an adversarial sequential detector by solving a minimax problem to find an optimal detector against the worst-case sequences from a generator. The generator captures the dependence i…
Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve continuous nonconvex-nonconcave formulations, a very basic question arises---"w…
Optimal algorithm for linear bandits on ellipsoids with minimax regret bound.
problem Linear stochastic bandits on ellipsoids.
method Novel sequential procedure to estimate norm of parameters, followed by an explore-and-commit strategy.
result Regret bound matches minimax lower bound with multiplicative constant.
New bounds on minimax regret for sequential probability assignment using logarithmic loss.
problem Minimizing regret in sequential probability assignment against arbitrary experts.
method Using self-concordance property of logarithmic loss to derive tight bounds.
result Tight bounds on minimax regret for various expert classes.
Study minimax regret in sequential probability assignment with and without side information.
problem Minimax regret analysis in sequential probability assignment.
method Upper and lower bounds on minimax regret using square-root entropy.
result Lower bound matches upper bound for Donsker classes, up to log factors.
Optimal algorithm for high-dimensional stochastic linear bandits with sparse parameters.
problem High-dimensional stochastic linear bandits with sparse parameters.
method Three-stage arm selection algorithm using thresholded Lasso for estimation.
result Achieves exact minimax optimality in cumulative regret.
New algorithms solve nonconvex-nonconcave minimax optimization problems.
problem Solving minimax optimization problems in machine learning.
method Two novel Newton-type algorithms for nonconvex-nonconcave minimax optimization.
result Proved local convergence at strict local minimax points.
Develops locally private methods for nonparametric contextual bandits.
problem Privacy concerns in sequential decision-making on sensitive data.
method Uniform-confidence-bound-type estimator and jump-start scheme.
result Minimax optimality of proposed methods supported by lower bounds.
GP-UCB performs suboptimally under certain conditions, as shown by a new regret lower bound.
problem The suboptimality of GP-UCB under polynomial effective optimism.
method Analysis of effective optimism level and new regret lower bound.
result GP-UCB is not minimax optimal under polynomial growth of effective optimism.
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…
The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for…
Recursive experts improve dynamic sequential learning systems.
problem Adapt to changing environments in sequential learning.
method Design hyper-experts that recursively merge to achieve optimal performance.
result Achieve minimax optimal regret bounds up to constant factors.
This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…
Study optimizes portfolio allocation policies using off-policy data and constraints.
problem Optimizing portfolio allocation policies under constraints using off-policy data.
method Solves a minimax objective with off-policy estimators and online learning to control constraint violations.
result Constructs near-optimal allocation policies for various regimes of operation and constraints.
New SGDA method speeds up nonconvex minimax optimization.
problem Improving convergence of nonconvex minimax optimization.
method SGDA with random reshuffling for nonconvex-PŁ objectives.
result Convergence rates faster than with-replacement SGDA.
This paper explores minimax-Bayes solutions for reinforcement learning problems.
problem How to select appropriate priors for decision making under uncertainty in sequential decision making.
method Study of minimax-Bayes solutions for various reinforcement learning problems.
result Minimax policies are more robust than standard priors.
Improving Generalization of Reinforcement Learning with Minimax Distributional Soft Actor-Criticcs.LG
Reinforcement learning (RL) has achieved remarkable performance in numerous sequential decision making and control tasks. However, a common problem is that learned nearly optimal policy always overfits to the training environment and may not be extended to situations never encountered during training. For practical app…
UCB algorithms improve on bandit problems with precise regret analysis and adaptive inference.
problem Understanding the performance and statistical inference of UCB algorithms in multi-armed bandit problems.
method Deterministic characterization of arm pulls and precise regret analysis.
result UCB algorithms' maximal regret deviates from minimax regret by a logarithmic factor, and the Lai-Robbins formula is exact only under specific conditions.
Transformers learn new tasks from few examples via optimal approximation.
problem Learning new tasks from limited examples using large language models.
method Developed approximation and generalization error bounds for transformers trained on nonparametric regression tasks.
result Transformers achieve minimax optimal estimation risk in context.
Optimizes quickest change detection with bounded means under ARL constraint.
problem Quickest detection of changepoints with bounded means under ARL constraint.
method Derives universal lower and upper bounds for detection delay.
result Achieves universal lower bound in the bounded mean detection setting.
We establish optimal rates for online regression for arbitrary classes of regression functions in terms of the sequential entropy introduced in (Rakhlin, Sridharan, Tewari, 2010). The optimal rates are shown to exhibit a phase transition analogous to the i.i.d./statistical learning case, studied in (Rakhlin, Sridharan,…
Study optimizes zero-order strongly convex function minimization with higher order smoothness.
problem Optimizing a strongly convex function with noisy evaluations.
method Randomized approximation of projected gradient descent with smoothing kernel.
result Upper bounds and minimax lower bounds for the algorithm, showing near-optimality.
The paper achieves nearly optimal regret bounds for contextual multinomial logit bandits.
problem The contextual multinomial logit (MNL) bandit problem with varying rewards.
method Established lower bounds and proposed OFU-MNL+ algorithm with matching upper bounds.
result Achieved minimax optimal regret bounds for both uniform and non-uniform reward settings.
New algorithm minimizes expert selection regret in partial bandit feedback.
problem Minimizing expert selection regret in partial bandit feedback.
method Develops a sequential minimax optimal algorithm for a generalized partial monitoring setting.
result Second order regret bounds against a general expert selection sequence.
We consider the problem of sequential prediction and provide tools to study the minimax value of the associated game. Classical statistical learning theory provides several useful complexity measures to study learning with i.i.d. data. Our proposed sequential complexities can be seen as extensions of these measures to …
The paper tackles minimax optimality in continuum contextual bandits with Hölder continuity.
problem Minimizing regret in a continuum of contexts with Hölder continuity.
method Proves a static-to-contextual regret conversion theorem and analyzes various dependency cases.
result Achieves minimax optimal contextual regret for convex and strongly convex bandits.
We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditi…
The paper addresses bias in fraud detection models by improving label recovery in payment networks.
problem Systematic bias in chargeback labels in payment networks.
method Formalizes the observation pipeline as a sequential missing-data problem with three stages and a corruption layer. Constructs the Sequential Triply Robust (STR) estimator to correct for all four impairments simultaneously.
result Achieves the semiparametric efficiency bound and provably dominates naive chargeback-based training in mean squared error.
Trust-aware MAB improves learning performance by accounting for human deviation.
problem Learning performance suffers when humans deviate from recommended policies due to lack of trust.
method Integrates a dynamic trust model into MAB framework, establishing minimax regret and proposing a two-stage trust-aware procedure.
result Proves near-optimal statistical guarantees for trust-aware MAB algorithms.
DARTS optimizes covariate selection in trials with limited data.
problem Limited budget for high-dimensional pretreatment data.
method Dynamic Adaptive Rerandomization via Thompson Sampling (DARTS).
result DARTS efficiently concentrates budget on informative features.
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees tha…
The paper addresses learner privacy in convex optimization with feedback.
problem Privacy risks from eavesdropping adversaries observing learner's queries.
method Optimally obfuscating learner's queries to make their learned optimal value hard to estimate.
result Query complexity overhead is additive in in the minimax formulation, multiplicative in in the Bayesian formulation.
Adaptive algorithm minimizes online prediction errors for irregular data.
problem Online adversarial regression with highly irregular prediction rules.
method Adaptive wavelet-based algorithm for Besov space regression.
result Minimax-optimal regret bounds in adversarial settings.
New approach transfers rewards learned in one environment to reinforcement learning in a new environment.
problem Transfer of rewards learned using inverse reinforcement learning from one environment to a new, different environment.
method Formulate the problem as a joint system of Bellman equations, develop minimax estimators for the target soft--function, solve the source and target system of equations jointly.
result The coupled approach removes the first-order influence of source Bellman residual error compared to the sequential approach.
Paper proposes a 1-bit mean estimation method with near-optimal sample complexity.
problem Distributed mean estimation with 1-bit communication constraints.
method Randomized and sequentially-chosen interval queries to estimate mean.
result Sample complexity bound matches minimax lower bound with logarithmic factors.
A novel decentralized algorithm improves minimax optimization in federated learning.
problem Minimax optimization in federated learning with data heterogeneity.
method Decentralized Gradient Tracking (K-GT-Minimax) for nonconvex-strongly-concave optimization.
result Demonstrates superior convergence rate for NC-SC minimax optimization.
Develops an online method for solving constrained optimization problems with debiasing techniques.
problem Online inference of solutions to constrained optimization problems with equality and inequality constraints.
method Stochastic Sequential Quadratic Programming (SSQP) with momentum debiasing.
result Achieves global almost-sure convergence and local asymptotic normality with optimal primal-dual limiting covariance.
This paper explores the possibility of near-optimally solving multi-agent, multi-task NP-hard planning problems with time-dependent rewards using a learning-based algorithm. In particular, we consider a class of robot/machine scheduling problems called the multi-robot reward collection problem (MRRC). Such MRRC problem…
The study reveals fundamental limits of fraud detection in card payment networks.
problem Fraud detection in card payment networks is challenging due to structural information impairments.
method Formalized card authorization as a sequential decision problem with delayed feedback, derived minimax regret lower bound.
result Improving issuer reporting quality or reducing censorship can yield larger reductions in the regret floor than increasing model complexity.
Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an asset on a given date in the future. In 1973, Black and Scholes proposed a valuati…
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
Two algorithms for linear contextual bandits with rare updates achieve optimal regret and efficiency.
problem Linear contextual bandits with infrequent parameter updates.
method Two practical algorithms with updates, BLCE-G and BLCE.
result Minimax-optimal regret with low computational complexity.