AlphaLoss: LLM-Driven Evolution of Robust and Interpretable Portfolio Optimization Objectives

In this paper, we introduce AlphaLoss, a novel framework that autonomously discovers robust portfolio optimization objectives by leveraging Large Language Models (LLMs) through an iterative process of generation, evaluation, and refinement. Unlike traditional approaches that rely on rigid heuristics such as mean-variance optimization, AlphaLoss integrates multiple components grounded in both classical financial theory and recent quantitative research. These components, as discovered by the evolutionary process, explicitly incorporate rolling window computations to ensure temporal stability and robust performance across varied market conditions. These include: (i) robust return estimation via winsorization, (ii) downside risk through semi-standard deviation, (iii) drawdown sensitivity via maximum drawdown and recovery duration penalties, (iv) conditional volatility inspired by GARCH, (v) entropy-based diversification, (vi) weight regularization using lasso, ridge, and max constraints, (vii) tail risk measures including VaR and CVaR, (viii) higher moment penalties for skewness and kurtosis, and (ix) temporal instability penalties to encourage stable allocations. AlphaLoss’s components are not manually engineered, but discovered and refined using LLMs inspired by recent advances in AI-driven scientific discovery. Through few-shot prompting and mutational refinement, the LLM autonomously proposes new loss components, evaluates them via historical backtesting, and iteratively improves the objective function based on empirical performance. The result is a multi-objective loss that balances return, risk, robustness, and implementability—yielding portfolios that outperform classical strategies under realistic conditions of estimation error, non-Gaussian returns, and dynamic market regimes.