Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
problem Online statistical inference of model parameters in stochastic optimization problems.
method Kiefer-Wolfowitz algorithm with random search directions, asymptotic distribution analysis.
result Developed valid confidence intervals for online statistical inference.
We consider the problem of designing an allocation rule or an "online learning algorithm" for a class of bandit problems in which the set of control actions available at each time s is a convex, compact subset of Rd. Upon choosing an action x at time s, the algorithm obtains a noisy value of the unkno…
McDiarmid's inequality under dependence via approximate tensorization of entropy
problem Dependent versions of McDiarmid's inequality
method Approximate tensorization of entropy (ATE)
result Derives McDiarmid's inequality for non-isotropic Gaussian random vectors
Paper analyzes error in stochastic approximation for discontinuous functions.
problem Estimating expected error in discontinuous stochastic approximation.
method Uses finite differences and O(n−1/5) error estimate for discontinuous functions. result Achieves error estimate of O(n−1/5) for discontinuous stochastic representation. Stochastic approximation algorithms show exponential progress bounds.
problem Analyzing the convergence of stochastic approximation algorithms.
method Developed geometric ergodicity proofs to establish exponential concentration bounds.
result Proved faster convergence rates for specific algorithms.
In online portfolio optimization the investor makes decisions based on new, continuously incoming information on financial assets (typically their prices). In our study we consider a learning algorithm, namely the Kiefer--Wolfowitz version of the Stochastic Gradient method, that converges to the log-optimal solution in…
We propose confidence sequences -- sequences of confidence intervals which are valid uniformly over time -- for quantiles of any distribution over a complete, fully-ordered set, based on a stream of i.i.d. observations. We give methods both for tracking a fixed quantile and for tracking all quantiles simultaneously. Sp…
EB-PCA reduces noise in high-dimensional PCA by estimating a joint prior distribution.
problem High-dimensional PCA noise in samples comparable to or larger than data.
method Empirical Bayes PCA using Kiefer-Wolfowitz MLE, random matrix theory, and AMP algorithm.
result EB-PCA achieves Bayes-optimal accuracy in spiked models and significantly improves over PCA in simulations and real data.
Enhanced DFO using adaptive batch-based FD estimates.
problem Derivative-free optimization with imprecise gradient estimates.
method Adaptive batch-based finite difference estimation and dynamic sampling strategy.
result Algorithm achieves convergence rate similar to KW and SPSA methods.
Optimal design for multinomial logit models improves assortment selection efficiency.
problem Optimal experimental design for multinomial logit models with feedback.
method Two complementary approaches: MILP reformulation and lifted design.
result Achieves statistical efficiency and scalability for MNL bandits.
Unified algorithm for stochastic optimization with time-varying momentum converges under general conditions.
problem Optimizing functions with time-varying gradients and biases.
method Unified algorithm using a time-varying momentum term.
result Convergence of the unified algorithm under general conditions.
We certify federated learning model performance under meta-distribution shifts.
problem Certifying model performance on unseen networks with heterogeneous distributions.
method Derive worst-case uniform guarantees for federated learning model's average loss and risk CDF.
result Asymptotically minimax optimal and privacy-preserving certification.
The construction by Du et al. (2019) implies that even if a learner is given linear features in Rd that approximate the rewards in a bandit with a uniform error of ε, then searching for an action that is optimal up to O(ε) requires examining essentially all actions. We use the Kiefer-Wolfowitz theorem to…
Paper addresses generalization error bounds for learning with censored feedback.
problem Impact of censored feedback on generalization error bounds.
method Derives an extension of DKW inequality for non-IID data due to censored feedback and uses it to bound generalization error.
result Existing generalization error bounds fail to account for censored feedback, necessitating new bounds.
New method for regression in high-dimensional space using mixture modeling and optimal transport.
problem Regression in high-dimensional space with unordered data.
method Mixture modeling and optimal transport for permutation recovery and denoising.
result Explicit upper bounds on mean squared denoising error for Gaussian noise.
Improved learning algorithm for first-price auctions reduces regret significantly.
problem Challenges in learning optimal bidding strategies for first-price auctions.
method Introduced novel ideas to achieve lower regret in sequential learning.
result Achieved log2(T) regret when opponents' bid distribution is known, and T1/3+ε regret in learning case.