Aggregating Strategies for Long-term Forecasting

Abstract

The article is devoted to investigating the application of aggregating algorithms to the problem of the long-term forecasting. We examine the classic aggregating algorithms based on the exponential reweighing. For the general Vovk's aggregating algorithm we provide its generalization for the long-term forecasting. For the special basic case of Vovk's algorithm we provide its two modifications for the long-term forecasting. The first one is theoretically close to an optimal algorithm and is based on replication of independent copies. It provides the time-independent regret bound with respect to the best expert in the pool. The second one is not optimal but is more practical and has O( √ T ) regret bound, where T is the length of the game.

Long-Term Online Smoothing Prediction Using Expert Advice

“…for each expert (n, τ ) such that 1 ≤ n ≤ N and τ ≤ T − d. Since l(n,τ) t = h t for t < τ + d, using ( 16), we obtain (17). △…”

“…The problem setting we investigate can be considered as the part of Decision-Theoretic Online Learning (DTOL) or Prediction with Expert Advice (PEA) framework (see e.g. [12,13,14,15,16,17] among others). In this framework the learner is usually called the aggregating algorithm.…”