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This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…
We address structured covariance estimation in Elliptical distribution. We assume it is a priori known that the covariance belongs to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of…
This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we…
We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…
We study quantum algorithms based on quantum (sub)gradient estimation using noisy function evaluation oracles, and demonstrate the first dimension-independent query complexities (up to poly-logarithmic factors) for zeroth-order convex…
In this paper we present a general convex optimization approach for solving high-dimensional multiple response tensor regression problems under low-dimensional structural assumptions. We consider using convex and weakly decomposable…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life…
Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional…
Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
Recent research has shown that quasar-convexity can be found in applications such as identification of linear dynamical systems and generalized linear models. Such observations have in turn spurred exciting developments in design and…
This paper deals with the grouped variable selection problem. A widely used strategy is to augment the negative log-likelihood function with a sparsity-promoting penalty. Existing methods include the group Lasso, group SCAD, and group MCP.…
This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…
We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…
In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed…
Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical…