Related papers: Stochastic Dimension-reduced Second-order Methods …

Multi-objective optimization (MOO) has received growing attention in applications that require learning under multiple criteria. However, the existing MOO formulations do not explicitly account for distributional shifts in the data. We…

This paper presents a novel algorithmic study with extensive numerical experiments of distributionally robust multistage convex optimization (DR-MCO). Following the previous work on dual dynamic programming (DDP) algorithmic framework for…

Distributionally robust optimization (DRO) is a powerful framework for training robust models against data distribution shifts. This paper focuses on constrained DRO, which has an explicit characterization of the robustness level. Existing…

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…

Deep reinforcement learning (DRL) is one of the promising approaches for introducing robots into complicated environments. The recent remarkable progress of DRL stands on regularization of policy, which allows the policy to improve stably…

To facilitate efficient learning, policy gradient approaches to deep reinforcement learning (RL) are typically paired with variance reduction measures and strategies for making large but safe policy changes based on a batch of experiences.…

We present a novel second-order trajectory optimization algorithm based on Stein Variational Newton's Method and Maximum Entropy Differential Dynamic Programming. The proposed algorithm, called Stein Variational Differential Dynamic…

A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…

Dimensionality reduction (DR) algorithms, which reduce the dimensionality of a given data set while preserving the information of the original data set as well as possible, play an important role in machine learning and data mining. Duan…

Recent results suggest that quantum computers possess the potential to speed up nonconvex optimization problems. However, a crucial factor for the implementation of quantum optimization algorithms is their robustness against experimental…

When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. In this work, we propose…

This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO). We generalize the usual consecutive dual dynamic programming (DDP) algorithm to DR-MCO and propose…

We study differentially private (DP) algorithms for smooth stochastic minimax optimization, with stochastic minimization as a byproduct. The holy grail of these settings is to guarantee the optimal trade-off between the privacy and the…

The minimax excess risk optimization (MERO) problem is a new variation of the traditional distributionally robust optimization (DRO) problem, which achieves uniformly low regret across all test distributions under suitable conditions. In…

We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…

In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and gradient and Hessian estimates are computed with noise. These estimates are produced by generic…

Zeroth-order (derivative-free) optimization attracts a lot of attention in machine learning, because explicit gradient calculations may be computationally expensive or infeasible. To handle large scale problems both in volume and dimension,…

We study the sample complexity of reducing reinforcement learning to a sequence of empirical risk minimization problems over the policy space. Such reductions-based algorithms exhibit local convergence in the function space, as opposed to…

In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $\epsilon$-stationary point within…

Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…