KellyBoost: Growth-Optimal Portfolio Construction with Gradient-Boosted Trees

Classification outperforms regression across matched machine learning models in portfolio construction. A stacking ensemble of gradient boosted tree, random forest, and neural network yields a value-weighted annualized Sharpe ratio of 1.83 for classification and 1.11 for regression. This outperformance persists in multiclass settings, across subsamples, and after transaction costs. Spanning tests show that classification retains economically large alphas after we control for regression, whereas regression alphas shrink substantially once we control for classification. These results indicate that classification extracts more return information than matched regression. Our diagnostics trace classification's advantage to sharper and more precise separation of return deciles.

Mean-variance portfolio optimization (MVO) is a central framework in data-driven asset management. A widely adopted approach is a two-stage framework that first predicts expected returns and then solves the optimization problem based on these predictions, with the predictive models trained by minimizing prediction errors. However, this objective of prediction is not aligned with the quality of the downstream portfolio decision. Decision-focused learning (DFL), which directly minimizes the downstream decision loss within the learning process, has thus emerged as a promising direction. However, existing DFL approaches to MVO rely on surrogate losses or constraint relaxations for tractability, creating a structural mismatch between predictive model training and the constrained MVO solved at evaluation. We propose a single-level optimization formulation that incorporates the Karush-Kuhn-Tucker (KKT) optimality conditions of the lower-level MVO into the upper-level learning problem. This formulation explicitly preserves the budget and short-sale constraints while remaining tractable for standard nonlinear optimization solvers. Rolling-window experiments on real-world ETF (Exchange Traded Funds) data across two asset universes with different correlation structures show that our method achieved the best performance on multiple investment metrics and also demonstrated performance improvement due to the proposed regularization.

Language models are saturating benchmarks for procedural tasks with narrow objectives. But they are increasingly being deployed in long-horizon, non-stationary environments with open-ended goals. In this paper we introduce KellyBench, an environment for evaluating sequential decision-making in sports betting markets. Agents are placed in a sequential simulation of the 2023-24 English Premier League season and tasked with maximising their long-term bankroll growth. They are given detailed historical data, including advanced statistics, lineups, and public odds. To succeed they must build machine learning models, identify edge in public markets, and adapt as the environment changes over time. We find that all frontier models evaluated lose money on average over the course of the season for five seeds. The best performing model achieves an average return of -8%, and many models experiencing ruin across seeds. To judge strategy sophistication, we use a human expert rubric to grade each model and find their approaches to be unsophisticated compared to human baselines; Claude Opus 4.6 achieves a rubric score of 26.5%, which means there is significant room for improvement. KellyBench is available as an open-access API endpoint at https://openreward.ai/GeneralReasoning/KellyBench.