arXiv research

The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.

This paper extends forecast reconciliation to non-linearly constrained time series.

In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample applications (e.g., grasping tasks and human-robot collaborations) further show …

New projection techniques reduce the frequency of projections in solving LCPs.

LinConTS improves regret and constraint violations in probabilistic linearly constrained bandits.

Unified framework for nonconvex matrix completion with linearly parameterized factors.

We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours is the first CD method that allows linear coupling constraints, without making th…

A new method solves large-scale sparse group square-root Lasso problems efficiently.

A new algorithm solves bilevel optimization with linear constraints.

LCW reduces activation shift in neural networks, improving training efficiency and generalization.

A new algorithm for solving constrained convex optimization problems efficiently.

New method solves constrained stochastic optimization problems efficiently.

New methods solve saddle point problems without line search.

In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the expected loss and not on finite-sum minimization, which is typically a much harder p…

Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate descent method that works well for smooth problems or those with separable nonsmooth …

New method calibrates neural network predictions for better reliability.

Neural networks learn vector fields constrained by linear operators.

A scalable framework optimizes multi-asset portfolios with constraints.

Hyper-parameter optimization remains as the core issue of Gaussian process (GP) for machine learning nowadays. The benchmark method using maximum likelihood (ML) estimation and gradient descent (GD) is impractical for processing big data due to its $O(n^3)$ complexity. Many sophisticated global or local approximation m…

Unified approach adjusts classifiers to meet system-level constraints.

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sam…

Boosted Difference of Convex Functions Algorithm solves VaR constrained portfolio optimization.

This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat(x), subject to a system of linear constraints of the form [A] . x = 0, where x is an unknown n-dimensional real vector to be determined up to an overall norm…

Heuristic algorithm for portfolio optimization reduces solve times to milliseconds.

We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gröbner bases. If successful, a push forward Gaussian process along the paramerization is the desired prior. We consider several exampl…

Unified framework for ESG-inclusive portfolio optimization and pricing.

The study quantifies how many objects can be linearly classified under all views.

New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.

Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some mome…

Block Coordinate Update (BCU) methods enjoy low per-update computational complexity because every time only one or a few block variables would need to be updated among possibly a large number of blocks. They are also easily parallelized and thus have been particularly popular for solving problems involving large-scale …

Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional time-series methods. Motivated by the study of human aging, we present an interpr…

First-order method solves stochastic bilevel optimization with linear constraints.

Enhances SSL with mixup and Lipschitz regularization.

New method tackles bilevel optimization with polyhedral constraints.

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…

Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.

Unified R packages for forecast reconciliation of constrained series.

In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global objective function and nodes are allowed to exchange information only with their n…

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods. This paper proposes two accelerated methods towards solving structured linearly co…

New algorithm reduces regret in sequential decision-making problems.

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 intractable, we first show that generic instances of the problem can be solved efficientl…

Extends GENO framework for GPU optimization of constrained ML problems.

Develops a theory to make learning solutions fair and safe.

T-Basis represents neural network tensors with fewer parameters.

Improved Frank-Wolfe algorithm for constrained convex optimization with nearest extreme point oracle.

A new method solves complex constrained minimax problems.

Bayesian approach for solving systems of linear PDEs with boundary conditions.

We introduce SCAL, an algorithm designed to perform efficient exploration-exploitation in any unknown weakly-communicating Markov decision process (MDP) for which an upper bound $c$ on the span of the optimal bias function is known. For an MDP with $S$ states, $A$ actions and $Γ\leq S$ possible next states, we prove a …