[
    {
        "id": "osp-22218",
        "type": "article-journal",
        "title": "Universal Dynamic Portfolios",
        "author": [
            {
                "family": "Zhang",
                "given": "Yujie"
            },
            {
                "family": "Wang",
                "given": "Yuxiang"
            },
            {
                "family": "Zhao",
                "given": "Peng"
            },
            {
                "family": "Jamieson",
                "given": "Kevin"
            }
        ],
        "URL": "https://omanscience.com/en/articles/universal-dynamic-portfolios",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "Cover's Universal Portfolio (Cover, 1991) matches the performance of the best constant rebalanced portfolio in hindsight. We generalize this framework to compete with an arbitrary comparator sequence $\\mathbf{u}_1,\\ldots,\\mathbf{u}_T$, leading to a dynamic regret minimization problem for the log loss where existing methods break down due to potentially unbounded gradients. The log loss is exp-concave, a curvature property that classically yields fast rates for static regret, yet we show that this advantage generally disappears in the dynamic setting. In particular, a linear-loss-type $\\sqrt{TP_T}$ dependence is unavoidable, where $P_T=\\sum_{t=2}^T\\lVert\\mathbf{u}_t-\\mathbf{u}_{t-1}\\rVert_1$ is the standard path length. This limitation stems from the coarse nature of $P_T$, which obscures finer spatial and temporal structure of the comparator sequence. We therefore introduce two structure-aware measures---the Jensen-Shannon distance for spatial structure and the JS$^q$-path length for temporal structure---under which faster rates are attainable when the comparator sequence has favorable structure. To achieve sharp bounds for both measures simultaneously, we develop Universal Dynamic Portfolio, a parameter-free method that combines a new Dirichlet Hedge algorithm with a fixed-share update, while retaining a near-optimal $P_T$ guarantee in the worst case. Finally, under an additional bounded-gradient assumption, we show that OPS admits the faster $T^{1/3}P_T^{2/3}$ dynamic regret rate over all comparator sequences. We attain this rate with a tractable proper algorithm that applies more broadly to general online exp-concave optimization over arbitrary compact convex domains."
    }
]