LLM-Based SQL Generation: Prompting, Self-Refinement, and Adaptive Weighted Majority Voting

Text-to-SQL has emerged as a prominent research area, particularly with the rapid advancement of large language models (LLMs). By enabling users to query databases through natural language rather than SQL, this technology significantly lowers the barrier to data analysis. However, generating accurate SQL from natural language remains challenging due to ambiguity in user queries, the complexity of schema linking, limited generalization across SQL dialects, and the need for domain-specific understanding. In this study, we propose a Single-Agent Self-Refinement with Ensemble Voting (SSEV) pipeline built on PET-SQL that operates without ground-truth data, integrating self-refinement with Weighted Majority Voting (WMV) and its randomized variant (RWMA). Experimental results show that the SSEV achieves competitive performance across multiple benchmarks, attaining execution accuracies of 85.5% on Spider 1.0-Dev, 86.4% on Spider 1.0-Test, and 66.3% on BIRD-Dev. Building on insights from the SSEV pipeline, we further propose ReCAPAgent-SQL (Refinement-Critique-Act-Plan agent-based SQL framework) to address the growing complexity of enterprise databases and real-world Text-to-SQL tasks. The framework integrates multiple specialized agents for planning, external knowledge retrieval, critique, action generation, self-refinement, schema linking, and result validation, enabling iterative refinement of SQL predictions through agent collaboration. ReCAPAgent-SQL's WMA results achieve 31% execution accuracy on the first 100 queries of Spider 2.0-Lite, demonstrating significant improvements in handling real-world enterprise scenarios. Overall, our work facilitates the deployment of scalable Text-to-SQL systems in practical settings, supporting better data-driven decision-making at lower cost and with greater efficiency.

Computing Pure-Strategy Nash Equilibria in a Two-Party Policy Competition: Existence and Algorithmic Approaches

We formulate two-party policy competition as a two-player non-cooperative game, generalizing Lin et al.'s work (2021). Each party selects a real-valued policy vector as its strategy from a compact subset of Euclidean space, and a voter's utility for a policy is given by the inner product with their preference vector. To capture the uncertainty in the competition, we assume that a policy's winning probability increases monotonically with its total utility across all voters, and we formalize this via an affine isotonic function. A player's payoff is defined as the expected utility received by its supporters. In this work, we first test and validate the isotonicity hypothesis through voting simulations. Next, we prove the existence of a pure-strategy Nash equilibrium (PSNE) in both one- and multi-dimensional settings. Although we construct a counterexample demonstrating the game's non-monotonicity, our experiments show that a decentralized gradient-based algorithm typically converges rapidly to an approximate PSNE. Finally, we present a grid-based search algorithm that finds an $ε$-approximate PSNE of the game in time polynomial in the input size and $1/ε$.

Generalized Mirror Descents in Congestion Games

Different types of dynamics have been studied in repeated game play, and one of them which has received much attention recently consists of those based on "no-regret" algorithms from the area of machine learning. It is known that dynamics based on generic no-regret algorithms may not converge to Nash equilibria in general, but to a larger set of outcomes, namely coarse correlated equilibria. Moreover, convergence results based on generic no-regret algorithms typically use a weaker notion of convergence: the convergence of the average plays instead of the actual plays. Some work has been done showing that when using a specific no-regret algorithm, the well-known multiplicative updates algorithm, convergence of actual plays to equilibria can be shown and better quality of outcomes in terms of the price of anarchy can be reached for atomic congestion games and load balancing games. Are there more cases of natural no-regret dynamics that perform well in suitable classes of games in terms of convergence and quality of outcomes that the dynamics converge to? We answer this question positively in the bulletin-board model by showing that when employing the mirror-descent algorithm, a well-known generic no-regret algorithm, the actual plays converge quickly to equilibria in nonatomic congestion games. Furthermore, the bandit model considers a probably more realistic and prevalent setting with only partial information, in which at each time step each player only knows the cost of her own currently played strategy, but not any costs of unplayed strategies. For the class of atomic congestion games, we propose a family of bandit algorithms based on the mirror-descent algorithms previously presented, and show that when each player individually adopts such a bandit algorithm, their joint (mixed) strategy profile quickly converges with implications.