Fixedshare

Fixed-share is an online learning algorithm designed to track the best predictor (or expert) in environments where the optimal choice may change over time. It extends the Hedge (or exponentially weighted) framework by incorporating a fixed amount of weight sharing across all experts, enabling the model to switch between experts with controlled flexibility.

In operation, the algorithm maintains a weight for each expert representing its current credibility. After observing the loss of each expert, the standard Hedge update increases or decreases weights based on performance. A subsequent sharing step distributes a fraction of the total weight, controlled by a parameter alpha in [0,1], among all experts. This sharing allows mass to migrate from currently favored experts to others, facilitating adaptation when the best expert changes. A common implementation computes intermediate scores, applies the exponential update, and then mixes the updated scores with a uniform distribution weighted by alpha.

The parameter alpha governs the degree of switching: small values favor stability and slow adaptation, while larger values permit quicker responsiveness to changes in which experts perform best. Theoretical results provide regret guarantees relative to the best sequence of experts under a bound on the number of switches. Specifically, the regret scales with the number of allowed switches as well as with the time horizon and the number of experts, yielding favorable performance when the optimal predictor changes infrequently compared to the total rounds.

Applications of fixed-share include online prediction tasks where the environment is non-stationary and a fixed pool of predictors is available. It is particularly relevant in tracking the best expert over time and in ensemble forecasting settings where different models may become relevant at different periods. The concept appears in online learning literature as a method for balancing stability with adaptability.