Related papers: A Curiously Effective Backtracking Strategy for Co…

With the development of pre-trained language models, the dense retrieval models have become promising alternatives to the traditional retrieval models that rely on exact match and sparse bag-of-words representations. Different from most…

A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…

LLM-based deep research agents are largely built on the ReAct framework. This linear design makes it difficult to revisit earlier states, branch into alternative search directions, or maintain global awareness under long contexts, often…

We present a novel class of proof-of-position algorithms: Tree-Proof-of-Position (T-PoP). This algorithm is decentralised, collaborative and can be computed in a privacy preserving manner, such that agents do not need to reveal their…

We consider Constrained Online Convex Optimization (COCO) with adversarially chosen constraints. At each round, the learner chooses an action before observing the loss and constraint function for that round. The goal is to achieve small…

We formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…

Conformal prediction can be used to construct prediction sets that cover the true outcome with a desired probability, but can sometimes lead to large prediction sets that are costly in practice. The most useful outcome is a singleton…

We introduce TROOP, a tree-based Riccati optimistic online planner, that is designed to generate near-optimal control laws for discrete-time switched linear systems with switched quadratic costs. The key challenge that we address is…

Constraint Optimization Problems (COP) pose intricate challenges in combinatorial problems usually addressed through Branch and Bound (B\&B) methods, which involve maintaining priority queues and iteratively selecting branches to search for…

Low-rank matrix recovery problems arise naturally as mathematical formulations of various inverse problems, such as matrix completion, blind deconvolution, and phase retrieval. Over the last two decades, a number of works have rigorously…

In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called…

Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates…

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…

The pairing heap is a simple "self-adjusting" implementation of a heap (priority queue). Inserting an item into a pairing heap or decreasing the key of an item takes O(1) time worst-case, as does melding two heaps. But deleting an item of…

Complex problems, whether in math, logic, or planning, are solved by humans through a sequence of steps where the result of one step informs the next. In this work, we adopt the perspective that the reasoning power of Transformers is…

In the framework of prediction of individual sequences, sequential prediction methods are to be constructed that perform nearly as well as the best expert from a given class. We consider prediction strategies that compete with the class of…

In this paper, by combining the algorithm New Q-Newton's method - developed in previous joint work of the author - with Armijo's Backtracking line search, we resolve convergence issues encountered by Newton's method (e.g. convergence to a…

Automated theorem proving systems built on Lean 4 increasingly rely on parallel tactic search over partially specified proofs, such as those generated by Draft-Sketch-Prove (DSP) pipelines. In current systems, each search branch…

Backtracking line search is foundational in numerical optimization. The basic idea is to adjust the step-size of an algorithm by a constant factor until some chosen criterion (e.g. Armijo, Descent Lemma) is satisfied. We propose a novel way…

LLM agents operating over massive, dynamic tool libraries rely on effective retrieval, yet standard single-shot dense retrievers struggle with complex requests. These failures primarily stem from the disconnect between abstract user goals…