This paper focuses on decentralized stochastic bilevel optimization (DSBO) where agents only communicate with their neighbors. We propose Decentralized Stochastic Gradient Descent and Ascent with Gradient Tracking (DSGDA-GT), a novel algorithm that only requires first-order oracles that are much cheaper than second-order oracles widely adopted in existing works. We further provide a finite-time convergence analysis … Read more
Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings of MSSA are limited: the multi-timescale analysis implies a slow convergence rate, whereas the single-timescale analysis relies on a stringent fixed point smoothness assumption. This paper … Read more
In recent years, the transition to clean bus fleets has accelerated. Although this transition might bring environmental and economic benefits, it requires a long-term strategic plan due to the large investment costs involved. This paper proposes a multi-stage stochastic program to optimize strategic plans for the clean bus fleet transition that explicitly considers the uncertainty … Read more
In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an \(\epsilon\)-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy \(\epsilon\). However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, … Read more
Understanding and predicting the electricity demand responses to prices are critical activities for system operators, retailers, and regulators. While conventional machine learning and time series analyses have been adequate for the routine demand patterns that have adapted only slowly over many years, the emergence of active consumers with flexible assets such as solar-plus-storage systems, and … Read more
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called “l0 norm”, which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing … Read more
We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the component of the step corrupted by the variance of the stochastic gradient estimates and a second which scales the entire step. We prove that this … Read more
We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. … Read more
We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables $\xi$ that appear in the problem through a set of discrete actions that we refer to as probing. Probing components of a random vector $\eta$ that is jointly-distributed with $\xi$ allows the … Read more
We consider a feature-based personalized pricing problem in which the buyer is strategic: given the seller’s pricing policy, the buyer can augment the features that they reveal to the seller to obtain a low price for the product. We model the seller’s pricing problem as a stochastic program over an infinite-dimensional space of pricing policies … Read more