Yuhang Bai

Yuxin Bai, Cecelia Shuai, Ashwin De Silva et al.

In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine learning algorithms, fails to account for dynamic data distributions and evolving objectives, often resulting in suboptimal performance. Prospective learning is a recently introduced mathematical framework that overcomes some of these limitations. We build on this framework to present preliminary results that improve the algorithm and numerical results, and extend prospective learning to sequential decision-making scenarios, specifically foraging. Code is available at: https://github.com/neurodata/prolearn2.

Yuhang Bai, Kristóf Bérczi

In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a spanning tree in which any two adjacent edges have distinct colors. Since finding such a tree is NP-hard in general, previous work often relied on minimum color degree conditions to guarantee the existence of properly colored spanning trees. While it is known that every connected edge-colored graph $G$ contains a properly colored tree of order at least $\min\{|V(G)|, 2δ^c(G)\}$, where $δ^c(G)$ denotes the minimum number of colors incident to a vertex, we study the algorithmic above-guarantee problem for properly colored trees. We provide a polynomial-time algorithm that constructs a properly colored tree of order at least $\min\{|V(G)|, 2δ^c(G)+1\}$ in a connected edge-colored graph $G$, whenever such a tree exists.