Related papers: Optimal Query Complexity of Secure Stochastic Conv…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
Network routing problems are common across many engineering applications. Computing optimal routing policies requires knowledge about network demand, i.e., the origin and destination (OD) of all requests in the network. However, privacy…
A constrained version of the online convex optimization (OCO) problem is considered. With slotted time, for each slot, first an action is chosen. Subsequently the loss function and the constraint violation penalty evaluated at the chosen…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…
We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety…
A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety…
We consider online learning in an adversarial, non-convex setting under the assumption that the learner has an access to an offline optimization oracle. In the general setting of prediction with expert advice, Hazan et al. (2016)…
Optimization-based controller tuning is challenging because it requires formulating optimization problems explicitly as functions of controller parameters. Safe learning algorithms overcome the challenge by creating surrogate models from…
We study the problem of finding an $\epsilon$-first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity for this task, assuming both the gradient and…
Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new…
We construct a family of functions suitable for establishing lower bounds on the oracle complexity of first-order minimization of smooth strongly-convex functions. Based on this construction, we derive new lower bounds on the complexity of…
Decentralized stochastic optimization is the basic building block of modern collaborative machine learning, distributed estimation and control, and large-scale sensing. Since involved data usually contain sensitive information like user…
A framework based on iterative coordinate minimization (CM) is developed for stochastic convex optimization. Given that exact coordinate minimization is impossible due to the unknown stochastic nature of the objective function, the crux of…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
We study non-smooth stochastic decentralized optimization problems over time-varying networks, where objective functions are distributed across nodes and network connections may intermittently appear or break. Specifically, we consider two…
Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost…
Distributed aggregative optimization underpins many cooperative optimization and multi-agent control systems, where each agent's objective function depends both on its local optimization variable and an aggregate of all agents' optimization…