arXiv research

New algorithm SFHC achieves near-optimal costs with predictions for non-convex optimization.

This study optimizes trading and arbitrage in decentralized finance's CPMs, revealing convexity costs and developing efficient strategies.

Optimal control in changing systems without strong convexity assumptions.

Efficient algorithm for unknown linear systems with convex costs.

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…

The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost function over a continuous space. We propose a stochastic mirror descent algorithm and …

Optimal crypto asset routing with CFMMs, including fixed costs.

New algorithms improve on consistency and robustness in convex function chasing with black-box advice.

In the field of optimal transport theory, an optimal map is known to be a gradient map of a potential function satisfying cost-convexity. In this paper, the Jacobian determinant of a gradient map is shown to be log-concave with respect to a convex combination of the potential functions when the underlying manifold is t…

Study weak super Ricci flow through neckpinch in metric measure spaces.

New algorithm controls linear systems with bandit feedback, achieving optimal regret.

A new method for optimal transport using neural ODEs that preserves marginal constraints.

New method calculates super-hedging prices with transaction costs.

OMGD algorithm optimizes online convex optimization with switching costs and delayed gradients.

New curvature measure for optimal transport with specific cost function.

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with …

Study uses weak transport for non-convex costs in fixed-income markets.

We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded above and below. This new condition is equivalent to the weak Ma-Trudinger-Wang condition when the cost is $C^4$. Moreover, we only require (n…

Let $X$ and $Y$ be domains of $\mathbb{R}^n$ equipped with respective probability measures $μ$ and $ν$. We consider the problem of optimal transport from $μ$ to $ν$ with respect to a cost function $c: X \times Y \to \mathbb{R}$. To ensure that the solution to this problem is smooth, it is necessary to make several ass…

Optimal maps, solutions to the optimal transportation problems, are completely determined by the corresponding c-convex potential functions. In this paper, we give simple sufficient conditions for a smooth function to be c-convex when the cost is given by minimizing a Lagrangian action.

New research extends optimal transport map breakdown properties to general costs.

The paper improves competitive and dynamic regret bounds for smoothed online learning.

Paper tackles online control of linear systems with unbounded noise.

Study on collaborative vs. non-collaborative online and bandit convex optimization.

Optimizes portfolios with discrete units using simulated annealing.

Optimizes routing in decentralized exchanges with gas fees.

Accelerated method finds critical points faster on manifolds.

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

Paper solves inverse optimal transport problem with convex optimization and neural network.

New proof of energy functional monotonicity via geodesics in measure space.

Optimal DP mechanisms for vector queries are found to be staircase distributions.

New method improves MAP inference for CGMs on path graphs, avoiding approximation and maintaining integrality.

The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric (constant trading volume) MI is…

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept has heretofore remained unexploited in convex optimization. To this end, we deve…

Paper proposes efficient cost functions for automated market makers in DeFi.

This paper accelerates distributed convex optimization by mitigating ill-conditioning issues.

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…

We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects…

This paper tackles cost-sensitive portfolio optimization under ambiguous return distributions.

Equivalent characterizations of multiportfolio time consistency are deduced for closed convex and coherent set-valued risk measures on $L^p(Ω,\mathcal F, P; R^d)$ with image space in the power set of $L^p(Ω,\mathcal F_t,P;R^d)$. In the convex case, multiportfolio time consistency is equivalent to a cocycle condition on…

Universal online optimization for dynamic environments using uniclass prediction.

We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $Ω(\sqrt{d})$ lower bound on the competitive ratio of any online algorithm, where $d$ is the dimension of the action space, we ask under what conditio…

A new method reduces communication costs in decentralized optimization.

In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the numéraire-based model and work with utility functions only supporting R+. Under the assumption of existence of consistent price sy…

A new parallel algorithm for learning optimal policies in MDPs with low communication costs.

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive rat…

Study timelike Ricci curvature bounds via optimal transport with Orlicz-type costs.

In this study, a novel sparsity-driven weighted ensemble classifier (SDWEC) that improves classification accuracy and minimizes the number of classifiers is proposed. Using pre-trained classifiers, an ensemble in which base classifiers votes according to assigned weights is formed. These assigned weights directly affec…