arXiv research

Optimistic algorithm reduces regret and constraint violations in online convex optimization with adversarial constraints.

Algorithm tackles constrained reinforcement learning with concave-convex and knapsack constraints.

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank a…

Paper solves high-order portfolio optimization with cardinality constraint.

Improved COCO algorithms with better constraint control.

This work shows neural networks can solve non-convex constraints problems.

This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. generated at each round and are disclosed to the decision maker only after the decision is made. Th…

The paper tackles MAP inference over non-convex constraints in safety-critical settings.

We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…

New single-loop algorithm tackles weakly convex constraints in stochastic optimization.

The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the objective is to find a low-rank approximation that meets rank and convex constraints, w…

New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.

Paper solves optimization problems with convex expectation constraints using a new algorithm.

Convex neural networks enforce convex constraints on weights and activations, improving generalization.

In this paper we consider the problem of minimizing area subject to a volume constraint in a given convex set.

Paper improves COCO problem, reducing constraint violation at the cost of slightly more regret.

Two new methods solve large-scale stochastic convex problems with linear constraints.

We show that many machine learning goals, such as improved fairness metrics, can be expressed as constraints on the model's predictions, which we call rate constraints. We study the problem of training non-convex models subject to these rate constraints (or any non-convex and non-differentiable constraints). In the non…

We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can be violated in intermediate rounds. For some user-defined trade-off parameter $β$…

Investigates convexity of minimizers under mass constraint using nonlocal perimeter and potential.

We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…

VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.

CoCoRL learns safe constraints from demonstrations with unknown rewards.

This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror des…

Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.

Optimal bounds on regret and constraint violation in adversarial COCO.

We describe two nonconventional algorithms for linear regression, called GAME and CLASH. The salient characteristics of these approaches is that they exploit the convex $\ell_1$-ball and non-convex $\ell_0$-sparsity constraints jointly in sparse recovery. To establish the theoretical approximation guarantees of GAME an…

The paper develops methods for time-varying constrained online convex optimization.

Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.

This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the proj…

The paper solves reverse isoperimetric problems for convex bodies with curvature constraints.

A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constr…

We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk…

Paper optimizes portfolio selection with ICX order constraints.

Study optimal portfolio management with periodic evaluations in stochastic models, considering convex constraints.

Comonotonic allocations are restored under certain constraints, improving risk-sharing.

New algorithm reduces regret and constraint violation in online convex optimization with predictions.

One-dimensional crystals have convex shapes under certain conditions.

Log-concavity proven for multinomial likelihoods under specific constraints.

New algorithms optimize actions under time-varying constraints without projecting.

New algorithm reduces constraint violation to $O(T^{1/3})$ while maintaining $O(\sqrt{T})$ regret.

This paper explores the nonconvexity of push-forward constraints in machine learning.

We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints corresponding to first-order stochastic dominance. We propose new discretization sch…

Study on policy testing in MDPs with lower bounds and new algorithm.

Upper bounds for circumradius in Hadamard surfaces with curvature constraints.

Study optimizes perimeter in convex domains with anisotropic constraints.

In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimiz…

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a nove…