3,028 research outputs found
Efficient Optimal Learning for Contextual Bandits
We address the problem of learning in an online setting where the learner
repeatedly observes features, selects among a set of actions, and receives
reward for the action taken. We provide the first efficient algorithm with an
optimal regret. Our algorithm uses a cost sensitive classification learner as
an oracle and has a running time , where is the number
of classification rules among which the oracle might choose. This is
exponentially faster than all previous algorithms that achieve optimal regret
in this setting. Our formulation also enables us to create an algorithm with
regret that is additive rather than multiplicative in feedback delay as in all
previous work
Optimal No-regret Learning in Repeated First-price Auctions
We study online learning in repeated first-price auctions with censored
feedback, where a bidder, only observing the winning bid at the end of each
auction, learns to adaptively bid in order to maximize her cumulative payoff.
To achieve this goal, the bidder faces a challenging dilemma: if she wins the
bid--the only way to achieve positive payoffs--then she is not able to observe
the highest bid of the other bidders, which we assume is iid drawn from an
unknown distribution. This dilemma, despite being reminiscent of the
exploration-exploitation trade-off in contextual bandits, cannot directly be
addressed by the existing UCB or Thompson sampling algorithms in that
literature, mainly because contrary to the standard bandits setting, when a
positive reward is obtained here, nothing about the environment can be learned.
In this paper, by exploiting the structural properties of first-price
auctions, we develop the first learning algorithm that achieves
regret bound when the bidder's private values are
stochastically generated. We do so by providing an algorithm on a general class
of problems, which we call monotone group contextual bandits, where the same
regret bound is established under stochastically generated contexts. Further,
by a novel lower bound argument, we characterize an lower
bound for the case where the contexts are adversarially generated, thus
highlighting the impact of the contexts generation mechanism on the fundamental
learning limit. Despite this, we further exploit the structure of first-price
auctions and develop a learning algorithm that operates sample-efficiently (and
computationally efficiently) in the presence of adversarially generated private
values. We establish an regret bound for this algorithm,
hence providing a complete characterization of optimal learning guarantees for
this problem
Contextual Bandits with Cross-learning
In the classical contextual bandits problem, in each round , a learner
observes some context , chooses some action to perform, and receives
some reward . We consider the variant of this problem where in
addition to receiving the reward , the learner also learns the
values of for all other contexts ; i.e., the rewards that
would have been achieved by performing that action under different contexts.
This variant arises in several strategic settings, such as learning how to bid
in non-truthful repeated auctions (in this setting the context is the decision
maker's private valuation for each auction). We call this problem the
contextual bandits problem with cross-learning. The best algorithms for the
classical contextual bandits problem achieve regret
against all stationary policies, where is the number of contexts, the
number of actions, and the number of rounds. We demonstrate algorithms for
the contextual bandits problem with cross-learning that remove the dependence
on and achieve regret (when contexts are stochastic with
known distribution), (when contexts are stochastic
with unknown distribution), and (when contexts are
adversarial but rewards are stochastic).Comment: 48 pages, 5 figure
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