Our analysis highlights sufficient properties for a regret minimization algorithm to be used as leader.

Top two algorithms arose as an adaptation of Thompson sampling to best arm identification in multi-armed bandit models for parametric families of arms. They select the next arm to sample from by randomizing among two candidate arms, a leader and a challenger. Despite their good empirical performance, theoretical guarantees for fixed-confidence best arm identification have only been obtained when the arms are Gaussian with known variances. In this paper, we provide a general analysis of top-two methods, which identifies desirable properties of the leader, the challenger, and the (possibly non-parametric) distributions of the arms. As a result, we obtain theoretically supported top-two algorithms for best arm identification with bounded distributions. Our proof method demonstrates in particular that the sampling step used to select the leader inherited from Thompson sampling can be replaced by other choices, like selecting the empirical best arm.

We study the problem of deciding whether, and when an organization should replace a trained incumbent model with a challenger relying on newly available features. We develop a unified economic and statistical framework that links learning-curve dynamics, data-acquisition and retraining costs, and discounting of future gains. First, we characterize the optimal switching time in stylized settings and derive closed-form expressions that quantify how horizon length, learning-curve curvature, and cost differentials shape the optimal decision. Second, we propose three practical algorithms--a one-shot baseline, a greedy sequential method, and a look-ahead sequential method. Using a real-world credit-scoring dataset with gradually arriving alternative data, we show that (i) optimal switching times vary systematically with cost parameters and learning-curve behavior, and (ii) the look-ahead sequential method outperforms other methods and is able to approach in value an oracle with full foresight. Finally, we establish finite-sample guarantees, including conditions under which the sequential look-ahead method achieve sublinear regret relative to that oracle. Our results provide an operational blueprint for economically sound model transitions as new data sources become available.

Correctness is an emergent property of systems where exposing error is cheaper than committing it. In dynamic, low-trust environments, autonomous AI agents benefit from delegating work to sub-agents, yet correctness cannot be assured through upfront specification or centralized oversight. We propose a protocol that enforces correctness through collateralized claims in a recursive verification game. Tasks are published as intents, and solvers compete to fulfill them. Selected solvers carry out tasks under risk, with correctness checked post hoc by verifiers. Any challenger can challenge a result by staking against it to trigger the verification process. Incorrect agents are slashed and correct opposition is rewarded, with an escalation path that penalizes erroneous verifiers themselves. When incentives are aligned across solvers, challengers, and verifiers, falsification conditions make correctness the Nash equilibrium.

AI self-evolution has long been envisioned as a path toward superintelligence, where models autonomously acquire, refine, and internalize knowledge from their own learning experiences. Yet in practice, unguided self-evolving systems often plateau quickly or even degrade as training progresses. These failures arise from issues such as concept drift, diversity collapse, and mis-evolution, as models reinforce their own biases and converge toward low-entropy behaviors. To enable models to self-evolve in a stable and controllable manner while minimizing reliance on human supervision, we introduce R-Few, a guided Self-Play Challenger-Solver framework that incorporates lightweight human oversight through in-context grounding and mixed training. At each iteration, the Challenger samples a small set of human-labeled examples to guide synthetic question generation, while the Solver jointly trains on human and synthetic examples under an online, difficulty-based curriculum. Across math and general reasoning benchmarks, R-Few achieves consistent and iterative improvements. For example, Qwen3-8B-Base improves by +3.0 points over R-Zero on math tasks and achieves performance on par with General-Reasoner, despite the latter being trained on 20 times more human data. Ablation studies confirm the complementary contributions of grounded challenger training and curriculum-based solver training, and further analysis shows that R-Few mitigates drift, yielding more stable and controllable co-evolutionary dynamics.

Motivated by applications to process massive datasets, we study streaming algorithms for pure exploration in Stochastic Multi Armed Bandits (MABs).

We propose a generic analysis of this type of algorithms, which puts forward new possibilities for the choice of leader and challenger used by the algorithm.

Games and puzzles play important pedagogical roles in STEM learning. New AI algorithms that can solve complex problems offer opportunities for scaffolded instruction in puzzle solving. This paper presents the ALLURE system, which uses an AI algorithm (Deep CubeA) to guide students in solving a common first step of the Rubik's Cube (i.e., the white cross). Using data from a pilot study we present preliminary findings about students' behaviors in the system, how these behaviors are associated with STEM skills - including spatial reasoning, critical thinking and algorithmic thinking. We discuss how data from ALLURE can be used in future educational data mining to understand how students benefit from AI assistance and collaboration when solving complex problems.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.