Shankar P. Sastry

Vidhi Zala, Varun Shankar, Shankar P. Sastry et al.

We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the coordinate deformation maps in both the interior and boundary of the curvilinear output mesh by using only scattered nodes on the boundary of the input mesh as data sites in an interpolation problem. Our technique produces high-quality meshes in the deformed domain even when the deformation maps are singular due to a new iterative algorithm based on modification of the RBF shape parameter. Due to the use of RBF interpolation, our technique is applicable to both 2D and 3D curvilinear mesh generation without significant modification.

Addison Kalanther, Sanika Bharvirkar, Shankar Sastry et al.

Multi-agent reinforcement learning (MARL) is increasingly used to design learning-enabled agents that interact in shared environments. However, training MARL algorithms in general-sum games remains challenging: learning dynamics can become unstable, and convergence guarantees typically hold only in restricted settings such as two-player zero-sum or fully cooperative games. Moreover, when agents have heterogeneous and potentially conflicting preferences, it is unclear what system-level objective should guide learning. In this paper, we propose a new MARL pipeline called Near-Potential Policy Optimization (NePPO) for computing approximate Nash equilibria in mixed cooperative--competitive environments. The core idea is to learn a player-independent potential function such that the Nash equilibrium of a cooperative game with this potential as the common utility approximates a Nash equilibrium of the original game. To this end, we introduce a novel MARL objective such that minimizing this objective yields the best possible potential function candidate and consequently an approximate Nash equilibrium of the original game. We develop an algorithmic pipeline that minimizes this objective using zeroth-order gradient descent and returns an approximate Nash equilibrium policy. We empirically show the superior performance of this approach compared to popular baselines such as MAPPO, IPPO and MADDPG.

Shankar Prasad Sastry

I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm infers Voronoi cells from seed vertices and constructs a linear function for the input data in and around each cell. As the algorithm does not explicitly compute the Voronoi diagram, it avoids the curse of dimensionality. An accuracy of around 98.2% on the MNIST dataset with 722,200 degrees of freedom (without data augmentation, convolution, or other geometric operators) demonstrates the applicability and scalability of the algorithm.