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Daniel Cao

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2 papers

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AAAI Conference 2025 Short Paper

Automating Thought of Search: A Journey Towards Soundness and Completeness (Student Abstract)

Daniel Cao
Michael Katz
Harsha Kokel
Kavitha Srinivas
Shirin Sohrabi

Large language models (LLMs) now turn their attention to search. Recently, Thought of Search (ToS) proposed defining the search space with code, having an LLM produce that code. ToS requires a human in the loop, collaboratively producing a sound successor function and goal test, achieving impressive 100% accuracy on all the tested datasets. In this work, we automate ToS (AutoToS), completely taking the human out of the loop of solving planning problems. AutoToS guides the language model step by step towards the generation of sound and complete search components, through feedback from both generic and domain specific unit tests. We achieve 100% accuracy, with minimal feedback iterations, using LLMs of various sizes on all evaluated domains.

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NeurIPS Conference 2025 Conference Paper

Efficiently Escaping Saddle Points under Generalized Smoothness via Self-Bounding Regularity

Daniel Cao
August Chen
Karthik Sridharan
Benjamin Tang

We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods. Smoothness is a restrictive assumption in machine learning in both theory and practice, motivating significant recent work on finding first order stationary points of functions satisfying generalizations of smoothness with first order methods. We develop a novel framework that lets us systematically study the convergence of a large class of first-order optimization algorithms (which we call decrease procedures) under generalizations of smoothness. We instantiate our framework to analyze the convergence of first order optimization algorithms to first and second order stationary points under generalizations of smoothness. As a consequence, we establish the first convergence guarantees for first order methods to second order stationary points under generalizations of smoothness. We demonstrate that several canonical examples fall under our framework, and highlight practical implications.

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