Related papers: Tight Dynamic Problem Lower Bounds from Generalize…
In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning.…
Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs…
We study the sample complexity of online reinforcement learning in the general \hzyrev{non-episodic} setting of nonlinear dynamical systems with continuous state and action spaces. Our analysis accommodates a large class of dynamical…
We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near the feasible set, we derive sharper worst-case complexity…
This paper presents an algorithm to solve the Soft k-Means problem globally. Unlike Fuzzy c-Means, Soft k-Means (SkM) has a matrix factorization-type objective and has been shown to have a close relation with the popular probability…
This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…
Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…
We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…
This work provides test error bounds for iterative fixed point methods on linear predictors -- specifically, stochastic and batch mirror descent (MD), and stochastic temporal difference learning (TD) -- with two core contributions: (a) a…
The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method…
The problem of reinforcement learning in an unknown and discrete Markov Decision Process (MDP) under the average-reward criterion is considered, when the learner interacts with the system in a single stream of observations, starting from an…
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…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
To deal with non-stationary online problems with complex constraints, we investigate the dynamic regret of online Frank-Wolfe (OFW), which is an efficient projection-free algorithm for online convex optimization. It is well-known that in…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum…
In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular…
Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For…
In this work, we study two natural generalizations of clique-width introduced by Martin F\"urer. Multi-clique-width (mcw) allows every vertex to hold multiple labels [ITCS 2017], while for fusion-width (fw) we have a possibility to merge…