20 research outputs found
Exploiting easy data in online optimization
International audienceWe consider the problem of online optimization, where a learner chooses a decision from a given decision set and suffers some loss associated with the decision and the state of the environment. The learner's objective is to minimize its cumulative regret against the best fixed decision in hindsight. Over the past few decades numerous variants have been considered, with many algorithms designed to achieve sub-linear regret in the worst case. However, this level of robustness comes at a cost. Proposed algorithms are often over-conservative, failing to adapt to the actual complexity of the loss sequence which is often far from the worst case. In this paper we introduce a general algorithm that, provided with a "safe" learning algorithm and an opportunistic "benchmark", can effectively combine good worst-case guarantees with much improved performance on "easy" data. We derive general theoretical bounds on the regret of the proposed algorithm and discuss its implementation in a wide range of applications, notably in the problem of learning with shifting experts (a recent COLT open problem). Finally, we provide numerical simulations in the setting of prediction with expert advice with comparisons to the state of the art
First-order regret bounds for combinatorial semi-bandits
We consider the problem of online combinatorial optimization under
semi-bandit feedback, where a learner has to repeatedly pick actions from a
combinatorial decision set in order to minimize the total losses associated
with its decisions. After making each decision, the learner observes the losses
associated with its action, but not other losses. For this problem, there are
several learning algorithms that guarantee that the learner's expected regret
grows as with the number of rounds . In this
paper, we propose an algorithm that improves this scaling to
, where is the total loss of the best
action. Our algorithm is among the first to achieve such guarantees in a
partial-feedback scheme, and the first one to do so in a combinatorial setting.Comment: To appear at COLT 201
Online Learning with Low Rank Experts
We consider the problem of prediction with expert advice when the losses of
the experts have low-dimensional structure: they are restricted to an unknown
-dimensional subspace. We devise algorithms with regret bounds that are
independent of the number of experts and depend only on the rank . For the
stochastic model we show a tight bound of , and extend it to
a setting of an approximate subspace. For the adversarial model we show an
upper bound of and a lower bound of
Following the Leader and Fast Rates in Linear Prediction: Curved Constraint Sets and Other Regularities
The follow the leader (FTL) algorithm, perhaps the simplest of all online learning algorithms, is known to perform well when the loss functions it is used on are positively curved. In this paper we ask whether there are other “lucky” settings when FTL achieves sublinear, “small” regret. In particular, we study the fundamental problem of linear prediction over a non-empty convex, compact domain. Amongst other results, we prove that the curvature of the boundary of the domain can act as if the losses were curved: In this case, we prove that as long as the mean of the loss vectors have positive lengths bounded away from zero, FTL enjoys a logarithmic growth rate of regret, while, e.g., for polyhedral domains and stochastic data it enjoys finite expected regret. Building on a previously known meta-algorithm, we also get an algorithm that simultaneously enjoys the worst-case guarantees and the bound available for FTL