Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG), quantifying the unavoidable discrepancy between a model's empirical fit and the population benchmark. Recovering the true population $R^2$, therefore, requires correcting observed predictive performance by this bound. Using a broad set of variables, including excess returns, yields, credit spreads, and valuation ratios, we find that the implied LLGs are large. This indicates that standard ML approaches can substantially understate true predictability in financial data. We also derive LLG-based refinements to the classic Hansen and Jagannathan (1991) bounds, analyze implications for parameter learning in general-equilibrium settings, and show that the LLG provides a natural mechanism for generating excess volatility.

We present three novel graph representations of planning tasks suitable for learning domain-independent heuristics using Graph Neural Networks (GNNs) to guide search. In particular, to mitigate the issues caused by large grounded GNNs we present the first method for learning domain-independent heuristics with only the lifted representation of a planning task. We also provide a theoretical analysis of the expressiveness of our models, showing that some are more powerful than STRIPS-HGN, the only other existing model for learning domain-independent heuristics. Our experiments show that our heuristics generalise to much larger problems than those in the training set, vastly surpassing STRIPS-HGN heuristics.

This document describes the design and implementation of the Tabletop Games framework (TAG), a Java-based benchmark for developing modern board games for AI research. TAG provides a common skeleton for implementing tabletop games based on a common API for AI agents, a set of components and classes to easily add new games and an import module for defining data in JSON format. At present, this platform includes the implementation of seven different tabletop games that can also be used as an example for further developments. Additionally, TAG also incorporates logging functionality that allows the user to perform a detailed analysis of the game, in terms of action space, branching factor, hidden information, and other measures of interest for Game AI research. The objective of this document is to serve as a central point where the framework can be described at length. TAG can be downloaded at: https://github.com/GAIGResearch/TabletopGames