Online Learning from Experts: Minimax Regret
نویسندگان
چکیده
In the last three lectures we have been discussing the online learning algorithms where we receive the instance x and then its label y for t = 1, ..., T . Specifically in the last lecture we talked about online learning from experts and online prediction. We saw many algorithms like Halving algorithm, Weighted Majority (WM) algorithm and lastly Weighted Majority Continuous (WMC) algorithm. We also saw bounds on the cumulative loss incurred by these algorithms. Today, we will focus on online prediction. For the WMC algorithm the setting is: we have N experts who predict the outcome (label) in [0,1], then we combine these predictions using a weighted average of these. Then we receive the true label and incur some loss (absolute loss in our setting), then we make an update to the weight vectors based on the loss. The intuition is that the higher the loss incurred by an expert, the more drastically we reduce its weight. For the WMC algorithm, we proved that:
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