New bounds show polyhedral surrogates are optimal for generalization.
problem Proving generalization rates for polyhedral loss functions.
method Developed two general results for polyhedral surrogates.
result Polyhedral surrogates provide linear surrogate regret bounds, translating directly to target rates.
We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.
problem Establishing linear regret bounds for convex smooth losses.
method Constructing a convex smooth surrogate loss using Fenchel-Young losses generated by the convolutional negentropy.
result We derive a smooth loss with a linear surrogate regret bound.
We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive classification risk. Two approaches to surrogate regret bounds are developed. The…
Enhanced H H H -consistency bounds derived under relaxed conditions.
problem Quantifying the relationship between zero-one estimation error and surrogate loss estimation error.
method Relaxing the condition on the surrogate loss conditional regret and presenting a general framework for establishing enhanced H H H -consistency bounds. result Derivation of more favorable H H H -consistency bounds in various scenarios. We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive new margin-based regret bounds in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an ef…
New algorithms handle online prediction with bandit and delayed feedback, improving regret bounds.
problem Achieving finite bounds on surrogate regret with limited feedback.
method Proposed algorithms for bandit and delayed feedback, including inverse-weighted gradient and pseudo-inverse matrix estimators.
result Achieved improved surrogate regret bounds of O ( K T ) O(\sqrt{KT}) O ( K T ) and O ( T 2 / 3 ) O(T^{2/3}) O ( T 2/3 ) . The problem of bipartite ranking, where instances are labeled positive or negative and the goal is to learn a scoring function that minimizes the probability of mis-ranking a pair of positive and negative instances (or equivalently, that maximizes the area under the ROC curve), has been widely studied in recent years. …
Gaptron algorithm reduces mistakes in online multiclass classification.
problem Online multiclass classification with limited information.
method Randomized first-order algorithm exploiting the gap between zero-one loss and surrogate losses.
result First linear time algorithm with O ( K T ) O(K\sqrt{T}) O ( K T ) expected regret. Optimal bounds on regret and constraint violation in adversarial COCO.
problem Minimizing regret and cumulative constraint violation in adversarial COCO.
method New surrogate loss function and Follow-the-Regularized-Leader/Online Gradient Descent.
result Achieved optimal O ( T ) O(\sqrt{T}) O ( T ) bounds on both regret and cumulative constraint violation. Paper improves Bayesian regret bounds for Thompson Sampling in reinforcement learning.
problem Improving Bayesian regret bounds for Thompson Sampling in reinforcement learning.
method Using a discrete set of surrogate environments and posterior consistency analysis, the authors derive an upper bound of order O ( H d l 1 T ) O(H\sqrt{d_{l_1}T}) O ( H d l 1 T ) . result The derived upper bound of O ( H d l 1 T ) O(H\sqrt{d_{l_1}T}) O ( H d l 1 T ) is a significant improvement over previous bounds. New algorithm uses machine learning to predict rewards for decision-making problems.
problem Sequential decision-making under uncertainty with scarce online data.
method Machine Learning-Assisted Upper Confidence Bound (MLA-UCB) algorithm.
result Proves to improve cumulative regret even with biased surrogate rewards.
Paper analyzes proper losses and their performance in machine learning tasks.
problem Understanding the performance of estimators and forecasters in machine learning tasks.
method Analyzes surrogate regret and convergence rates for strictly proper losses.
result Strongly proper losses achieve the optimal convergence rate.
Distributed Thompson sampling improves regret convergence in constrained communication networks.
problem Maximizing a black-box function with multi-agent Bayesian optimization under communication constraints.
method Distributed Thompson sampling using Gaussian processes, with theoretical bounds on regret convergence.
result Theoretical bounds on Bayesian average and simple regret depend on communication graph structure and are applicable in constrained networks.
New algorithm reduces online logistic regression regret without exponential constant.
problem Improper learning in online logistic regression with logarithmic regret.
method Regularized empirical risk minimization with surrogate losses.
result Regret scaling as O(B log(Bn)) with low computational complexity.
Improved online learning with time-varying constraints for complex domains.
problem Constrained online convex optimization with time-varying constraints.
method Constructing a composite surrogate loss and using the online Frank-Wolfe method.
result Novel regret and cumulative constraint violation bounds for strongly convex losses.
P-BO reduces black-box adversarial attacks by 10x with Bayesian optimization and function prior.
problem Efficiently generating adversarial examples against black-box models.
method Prior-guided Bayesian Optimization (P-BO) with a function prior initialized from a surrogate model.
result Significantly reduces the number of queries needed for adversarial attacks.
New bounds on IDS for RL show how to balance computation and learning efficiency.
problem Understanding and optimizing information-directed sampling (IDS) for reinforcement learning.
method Developed novel information-theoretic tools to bound information ratio and cumulative information gain.
result Derived prior-free Bayesian regret bounds for IDS in tabular finite-horizon MDPs and improved computational efficiency.
The paper improves bounds on regret in Gaussian process bandits.
problem Sequential optimization of expensive, possibly non-convex functions with noisy feedback.
method Analyzes maximal information gain and decay rates of GP kernel eigenvalues to improve regret bounds.
result General bounds on maximal information gain and improved regret bounds for various settings, including Matérn kernels.
This paper develops convex surrogates for optimizing the multi-label F-measure.
problem Optimizing the F-measure for multi-label classification is computationally hard.
method Designing convex surrogate losses calibrated for the F-measure.
result The F-measure for multi-label problems has a rank of at most s 2 + 1 s^2+1 s 2 + 1 . New algorithm optimizes Hölder smooth functions in RKHS with tighter regret bounds.
problem Optimizing Hölder smooth functions in RKHS with bounded norm.
method Proposes a new algorithm ( exttt{LP-GP-UCB}) using Local Polynomial (LP) estimators and multi-scale UCB.
result Derives high probability bounds on simple and cumulative regret, matching optimal performance for SE kernel and uniformly tighter bounds for Matérn kernels.
Paper establishes no-regret property for practical EGO optimization.
problem No theoretical bounds on cumulative regret for practical EGO.
method Introduced practical EGO with a positive nugget, analyzed its regret bounds.
result Practical EGO is a no-regret algorithm with sublinear regret bounds.
Improved algorithm reduces communication rounds for distributed online learning.
problem Complicated constraints in distributed online learning with locally light computations.
method Proposed D-BOCG algorithm with delayed update mechanism and redefined surrogate loss function.
result Achieved O ( T 3 / 4 ) O(T^{3/4}) O ( T 3/4 ) regret bound with O ( T ) O(\sqrt{T}) O ( T ) communication rounds for convex losses. Improved BO algorithms reduce prediction error under Gaussian noise.
problem Reducing prediction error in Bayesian optimization with Gaussian noise.
method Established new prediction error bounds for Gaussian process under frequentist setting.
result Proved improved convergence rates of cumulative regret for GP-UCB and GP-TS.
Study optimizes pricing under uncertainty and capacity constraints.
problem Optimizing pricing decisions under demand uncertainty and capacity constraints.
method Analyzes linear demand, stochastic noise, and finite capacity; uses certified demand forecasts and control variates.
result Certified demand forecasts reduce regret from O ( T ) O(\sqrt{T}) O ( T ) to O ( log T ) O(\log T) O ( log T ) under certain conditions. Bayesian optimization on networks using Gaussian process models.
problem Optimizing expensive black-box functions on network structures.
method Developed Bayesian optimization algorithms with Gaussian process surrogates tailored to network geometry.
result Established regret bounds for smooth objective functions and analyzed practical cases.
We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are rela…
New algorithms reduce regret for convex bandits with small comparator norms.
problem Optimizing in bandit convex optimization with varying comparator norms.
method Developed algorithms using techniques from full-information setting and new gradient estimators.
result Regret bounds are small when comparator norm is small.
We consider the problem of rank loss minimization in the setting of multilabel classification, which is usually tackled by means of convex surrogate losses defined on pairs of labels. Very recently, this approach was put into question by a negative result showing that commonly used pairwise surrogate losses, such as ex…
New method tackles online DR-submodular maximization with improved regret guarantees.
problem Online maximization of non-monotone DR-submodular functions over down-closed convex sets.
method 1/e-linearization through exponential reparametrization, surrogate potential, and reduction to online linear optimization.
result Achieves O ( T 1 / 2 ) O(T^{1/2}) O ( T 1/2 ) static regret with single gradient query per round, improving state of the art. New method achieves both universality and adaptivity in online convex optimization.
problem Achieve optimal regret guarantees without prior knowledge of function curvature.
method Introduces UniGrad, a novel approach that achieves both universality and adaptivity.
result Achieves universal regret guarantees that adapt to gradient variation.
New algorithm reduces regret bounds for Bayesian optimization with unknown hyperparameters.
problem Optimizing black-box functions with unknown hyperparameters, especially length scale.
method Length Scale Balancing (LB) - aggregating multiple surrogate models with varying length scales.
result LB achieves a regret bound only logaritically away from the oracle algorithm.
Optimizes functions on manifolds using Gaussian processes and graph models.
problem Optimizing functions on unknown manifolds with limited data.
method Graph Gaussian process surrogate model for sequential optimization.
result Established regret bounds for the proposed algorithm.
Study shows uncertainty calibration improves BO performance, but not as much as model type.
problem Effect of model uncertainties on Bayesian optimization performance.
method Extensive study comparing different surrogate models and their uncertainty calibration.
result Gaussian Processes outperform other models in BO, and uncertainty calibration does not significantly improve regret.
In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an O ( T ( 1 + P T ) ) O(\sqrt{T}(1+P_T)) O ( T ( 1 + P T )) dynamic regret, where T T T is the number of iterations and P T P_T P T is the path-le…
End-to-end framework learns LLM routing from observational data.
problem Compounding errors in decoupled approaches and reliance on full-feedback data.
method Causal end-to-end framework minimizing decision-making regret from observational data.
result Method outperforms existing baselines across different embedding models.
New framework analyzes regret in guided diffusion for optimizing structured inputs.
problem Understanding regret behavior in guided-diffusion black-box optimization for structured design problems.
method Developed a certificate-based expected simple-regret framework that avoids assumptions breaking down in modern diffusion BO pipelines.
result Explains how exponential and polynomial convergence can arise from mass lift in near-optimal designs.
Unified analysis of kernel-based and locally adaptive bandit optimization methods.
problem Performance of bandit optimization algorithms in RKHS functions.
method Investigates the relationship between kernel regularity and algorithmic performance, characterizing spectral properties of various kernels.
result Unified framework for analyzing kernel-based and locally adaptive bandit algorithms, deriving explicit regret bounds.
Paper tackles federated learning with personalised bandit algorithms.
problem Optimizing local and global objectives in a heterogeneous environment.
method Surrogate objective function combining client preferences and global knowledge; phase-based elimination algorithm.
result Achieves sublinear regret with logarithmic communication overhead.
A smart method predicts and optimizes decisions online with resource constraints.
problem Online decision-making with resource constraints.
method Combines prediction and optimization with dual update using mirror descent.
result Regret bounds and convergence rates for general convex feasible regions.
Optimal vehicle repositioning policy found for shared mobility services.
problem Matching fixed supply with spatial customer demand under uncertain and correlated demand.
method Base-stock repositioning policy, asymptotic optimality, regret analysis, adaptive repositioning algorithm.
result Surrogate Optimization and Adaptive Repositioning algorithm achieves optimal regret of O ( n 2.5 T ) O(n^{2.5} \sqrt{T}) O ( n 2.5 T ) . Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
Study on H H H -consistency bounds for machine learning surrogates.
problem Estimating target loss error relative to surrogate loss error in machine learning.
method Developed H H H -consistency bounds for various surrogates and loss functions. result Stronger guarantees than existing methods, offering distribution-dependent and -independent bounds.
Paper proposes an online learning method with multi-level adaptivity for diverse loss functions.
problem Online learning with unknown types and curvatures of functions.
method Multi-layer online ensemble approach with gradient variations.
result Achieves improved regret bounds for different types of loss functions.
Algorithm finds a simplified model for reinforcement learning under agent limitations.
problem Finding a simple model that approximates the true model for reinforcement learning.
method Uses rate-distortion theory to compute an approximately-value-equivalent, lossy compression of the environment.
result Proves an information-theoretic, Bayesian regret bound for the algorithm.
Paper bounds convergence rate of adversarial surrogate risk.
problem Vulnerability of binary classification models to adversarial attacks.
method Characterizes conditions for adversarial consistency and provides surrogate risk bounds.
result Surrogate risk bounds quantify the rate of convergence of adversarial classification risk.
Proposes efficient Bayesian logistic regression for large sparse datasets.
problem Infeasibility of theoretical Bayesian methods for large sparse feature sets.
method Low complexity analytical approximations for sparse online logistic and probit regressions.
result Empirical results show superior performance compared to more complex methods.
A standard introduction to online learning might place Online Gradient Descent at its center and then proceed to develop generalizations and extensions like Online Mirror Descent and second-order methods. Here we explore the alternative approach of putting Exponential Weights (EW) first. We show that many standard meth…
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1 / δ 1/δ 1/ δ with probability δ δ δ .