More recently, Newton-type methods using sparsified Hessian matrices have demonstrated promising results on OT computation, but there still remain a lot of unresolved open questions.

Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been significant effort towards the design of scalable approximation algorithms.

The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this approach to arbitrary numbers of objectives and compare its performance to scalar weighted sum methods during competitive motion planning. Explainable Artificial Intelligence (XAI) software is used to aid in the analysis of high dimensional decision-making data. State-space Exploration of Multidimensional Boundaries using Adherence Strategies (SEMBAS) is applied to explore performance modes in the parameter space as a sensitivity study for the baseline and proposed frameworks. While some works have explored aspects of game theoretic planning and intelligent systems validation separately, we combine each of these into a novel and comprehensive simulation pipeline. This integration demonstrates a dramatic improvement of the vector cost method over scalarization and offers an interpretable and generalizable framework for robotic behavioral planning. Code available at https://github.com/toazbenj/race_simulation. The video companion to this work is available at https://tinyurl.com/vectorcostvideo.

Recent work has extended the theoretical analysis of boosting algorithms to multi-class problems and to online settings.

Importantly, in practice, one can only compute points which approximately satisfy necessary optimality conditions, leading to the question: are such points also approximately optimal?

We address cost identification in a finite-horizon linear quadratic Gaussian game. We characterize the set of cost parameters that generate a given Nash equilibrium policy. We propose a backpropagation algorithm to identify the time-varying cost parameters. We derive a probabilistic error bound when the cost parameters are identified from finite trajectories. We test our method in numerical and driving simulations. Our algorithm identifies the cost parameters that can reproduce the Nash equilibrium policy and trajectory observations.

We present a Julia-based interface to the precompiled HALLaR and cuHALLaR binaries for large-scale semidefinite programs (SDPs). Both solvers are established as fast and numerically stable, and accept problem data in formats compatible with SDPA and a new enhanced data format taking advantage of Hybrid Sparse Low-Rank (HSLR) structure. The interface allows users to load custom data files, configure solver options, and execute experiments directly from Julia. A collection of example problems is included, including the SDP relaxations of the Matrix Completion and Maximum Stable Set problems.