Aggregating Strategies for Long-term Forecasting

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 $O(\sqrt{T})$ regret bound, where $T$ is the length of the game.Comment: 20 pages, 4 figure

Long-Term Online Smoothing Prediction Using Expert Advice

For the prediction with experts' advice setting, we construct forecasting algorithms that suffer loss not much more than any expert in the pool. In contrast to the standard approach, we investigate the case of long-term forecasting of time series and consider two scenarios. In the first one, at each step $t$ the learner has to combine the point forecasts of the experts issued for the time interval $[t+1, t+d]$ ahead. Our approach implies that at each time step experts issue point forecasts for arbitrary many steps ahead and then the learner (algorithm) combines these forecasts and the forecasts made earlier into one vector forecast for steps $[t+1,t+d]$. By combining past and the current long-term forecasts we obtain a smoothing mechanism that protects our algorithm from temporary trend changes, noise and outliers. In the second scenario, at each step $t$ experts issue a prediction function, and the learner has to combine these functions into the single one, which will be used for long-term time-series prediction. For each scenario, we develop an algorithm for combining experts forecasts and prove $O(\ln T)$ adversarial regret upper bound for both algorithms.Comment: 22 pages, 1 figur

Understanding Cyber Athletes Behaviour Through a Smart Chair: CS:GO and Monolith Team Scenario

eSports is the rapidly developing multidisciplinary domain. However, research and experimentation in eSports are in the infancy. In this work, we propose a smart chair platform - an unobtrusive approach to the collection of data on the eSports athletes and data further processing with machine learning methods. The use case scenario involves three groups of players: `cyber athletes' (Monolith team), semi-professional players and newbies all playing CS:GO discipline. In particular, we collect data from the accelerometer and gyroscope integrated in the chair and apply machine learning algorithms for the data analysis. Our results demonstrate that the professional athletes can be identified by their behaviour on the chair while playing the game.Comment: 6 pages, 6 figure

Integral Mixability: a Tool for Efficient Online Aggregation of Functional and Probabilistic Forecasts

In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially concave) loss functions to compare functional predictions and prove that these adaptations are also mixable (exp-concave). We call this phenomena integral mixability (exp-concavity). As an application of our main result, we prove that various loss functions used for probabilistic forecasting are mixable (exp-concave). The considered losses include Sliced Continuous Ranking Probability Score, Energy-Based Distance, Optimal Transport Costs & Sliced Wasserstein-2 distance, Beta-2 & Kullback-Leibler divergences, Characteristic function and Maximum Mean Discrepancies

Adaptive Hedging under Delayed Feedback

The article is devoted to investigating the application of hedging strategies to online expert weight allocation under delayed feedback. As the main result, we develop the General Hedging algorithm $\mathcal{G}$ based on the exponential reweighing of experts' losses. We build the artificial probabilistic framework and use it to prove the adversarial loss bounds for the algorithm $\mathcal{G}$ in the delayed feedback setting. The designed algorithm $\mathcal{G}$ can be applied to both countable and continuous sets of experts. We also show how algorithm $\mathcal{G}$ extends classical Hedge (Multiplicative Weights) and adaptive Fixed Share algorithms to the delayed feedback and derive their regret bounds for the delayed setting by using our main result.Comment: 38 pages, 11 figure