Learning-Augmented Online Portfolio Selection: Optimal Robustness-Consistency Tradeoffs

We study learning-augmented online portfolio selection (OPS), where an investor uses predictions to improve wealth while remaining protected against unreliable advice. In frictionless markets, we characterize the optimal tradeoff between robustness (wealth under arbitrary predictions) and consistency (wealth under perfect predictions) tied to the geometric mean, and show that the optimal tradeoff admits a tractable online characterization. We further quantify how performance interpolates between these endpoints under imperfect predictions by smoothness guarantees. Under transaction costs, we give exact robust-trading certificates and, to our knowledge, the first learning-augmented OPS impossibility under costs: for any positive cost, no GM-robust policy can be maximally consistent under exact predictions. Lastly, we show that a cost-aware greedy rule remains Pareto-optimal.