arXiv subjects

Haodong Sun

Publications and source records attributed to Haodong Sun.

4 recordsLinked to original sources

arXiv2021

Approximating the Optimal Transport Plan via Particle-Evolving Method

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately, computing the Wasserstein distance between two continuous probability measures always suffers from heavy computational intractability. In this paper, we propose an innovative algorithm that iteratively evolves a particle system to match the optimal transport plan for two given continuous probability measures. The derivation of the algorithm is based on the construction of the gradient flow of an Entropy Transport Problem which could be naturally understood as a classical Wasserstein optimal transport problem with relaxed marginal constraints. The algorithm comes with theoretical analysis and empirical evidence.

math.OC↗

arXiv2020

Risk-sensitive Dynkin games with heterogeneous Poisson random intervention times

The paper solves constrained Dynkin games with risk-sensitive criteria, where two players are allowed to stop at two independent Poisson random intervention times, via the theory of backward stochastic differential equations. This generalizes the previous work of [Liang and Sun, Dynkin games with Poisson random intervention times, SIAM Journal on Control and Optimization, 2019] from the risk-neutral criteria and common signal times for both players to the risk-sensitive criteria and two heterogenous signal times. Furthermore, the paper establishes a connection of such constrained risk-sensitive Dynkin games with a class of stochastic differential games via Krylov's randomized stopping technique.

math.OC↗

arXiv2020

Learning Cost Functions for Optimal Transport

Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem, which can be further augmented by any customizable regularization. We provide a comprehensive characterization of the properties of inverse OT, including uniqueness of solutions. We also develop two numerical algorithms, one is a fast matrix scaling method based on the Sinkhorn-Knopp algorithm for discrete OT, and the other one is a learning based algorithm that parameterizes the cost function as a deep neural network for continuous OT. The novel framework proposed in the work avoids repeatedly solving a forward OT in each iteration which has been a thorny computational bottleneck for the bi-level optimization in existing inverse OT approaches. Numerical results demonstrate promising efficiency and accuracy advantages of the proposed algorithms over existing state-of-the-art methods.

cs.LG↗

arXiv2019

Dynkin games with Poisson random intervention times

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The paper further applies the model to study the optimal conversion and calling strategies of convertible bonds, and their asymptotics when the Poisson intensity goes to infinity.

math.OC↗