41,966 research outputs found
Efficient tracking of a growing number of experts
International audienceWe consider a variation on the problem of prediction with expert advice, where new forecasters that were unknown until then may appear at each round. As often in prediction with expert advice, designing an algorithm that achieves near-optimal regret guarantees is straightforward, using ag-gregation of experts. However, when the comparison class is sufficiently rich, for instance when the best expert and the set of experts itself changes over time, such strategies naively require to maintain a prohibitive number of weights (typically exponential with the time horizon). By contrast, designing strategies that both achieve a near-optimal regret and maintain a reasonable number of weights is highly non-trivial. We consider three increasingly challenging objectives (simple regret, shifting regret and sparse shifting regret) that extend existing notions defined for a fixed expert ensemble; in each case, we design strategies that achieve tight regret bounds, adaptive to the parameters of the comparison class, while being computationally inexpensive. Moreover, our algorithms are anytime , agnostic to the number of incoming experts and completely parameter-free. Such remarkable results are made possible thanks to two simple but highly effective recipes: first the " abstention trick " that comes from the specialist framework and enables to handle the least challenging notions of regret, but is limited when addressing more sophisticated objectives. Second, the " muting trick " that we introduce to give more flexibility. We show how to combine these two tricks in order to handle the most challenging class of comparison strategies
Prediction with Expert Advice under Discounted Loss
We study prediction with expert advice in the setting where the losses are
accumulated with some discounting---the impact of old losses may gradually
vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm
for Regression to this case, propose a suitable new variant of exponential
weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte
Improved Second-Order Bounds for Prediction with Expert Advice
This work studies external regret in sequential prediction games with both
positive and negative payoffs. External regret measures the difference between
the payoff obtained by the forecasting strategy and the payoff of the best
action. In this setting, we derive new and sharper regret bounds for the
well-known exponentially weighted average forecaster and for a new forecaster
with a different multiplicative update rule. Our analysis has two main
advantages: first, no preliminary knowledge about the payoff sequence is
needed, not even its range; second, our bounds are expressed in terms of sums
of squared payoffs, replacing larger first-order quantities appearing in
previous bounds. In addition, our most refined bounds have the natural and
desirable property of being stable under rescalings and general translations of
the payoff sequence
Adaptation to Easy Data in Prediction with Limited Advice
We derive an online learning algorithm with improved regret guarantees for
`easy' loss sequences. We consider two types of `easiness': (a) stochastic loss
sequences and (b) adversarial loss sequences with small effective range of the
losses. While a number of algorithms have been proposed for exploiting small
effective range in the full information setting, Gerchinovitz and Lattimore
[2016] have shown the impossibility of regret scaling with the effective range
of the losses in the bandit setting. We show that just one additional
observation per round is sufficient to circumvent the impossibility result. The
proposed Second Order Difference Adjustments (SODA) algorithm requires no prior
knowledge of the effective range of the losses, , and achieves an
expected regret guarantee, where is the time horizon and is the number
of actions. The scaling with the effective loss range is achieved under
significantly weaker assumptions than those made by Cesa-Bianchi and Shamir
[2018] in an earlier attempt to circumvent the impossibility result. We also
provide a regret lower bound of , which almost
matches the upper bound. In addition, we show that in the stochastic setting
SODA achieves an pseudo-regret bound that holds simultaneously
with the adversarial regret guarantee. In other words, SODA is safe against an
unrestricted oblivious adversary and provides improved regret guarantees for at
least two different types of `easiness' simultaneously.Comment: Fixed a mistake in the proof and statement of Theorem
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