1,441 research outputs found
PAC-Bayesian Analysis of the Exploration-Exploitation Trade-off
We develop a coherent framework for integrative simultaneous analysis of the
exploration-exploitation and model order selection trade-offs. We improve over
our preceding results on the same subject (Seldin et al., 2011) by combining
PAC-Bayesian analysis with Bernstein-type inequality for martingales. Such a
combination is also of independent interest for studies of multiple
simultaneously evolving martingales.Comment: On-line Trading of Exploration and Exploitation 2 - ICML-2011
workshop. http://explo.cs.ucl.ac.uk/workshop
Heterogeneous Stochastic Interactions for Multiple Agents in a Multi-armed Bandit Problem
We define and analyze a multi-agent multi-armed bandit problem in which
decision-making agents can observe the choices and rewards of their neighbors.
Neighbors are defined by a network graph with heterogeneous and stochastic
interconnections. These interactions are determined by the sociability of each
agent, which corresponds to the probability that the agent observes its
neighbors. We design an algorithm for each agent to maximize its own expected
cumulative reward and prove performance bounds that depend on the sociability
of the agents and the network structure. We use the bounds to predict the rank
ordering of agents according to their performance and verify the accuracy
analytically and computationally
PAC-Bayesian Analysis of Martingales and Multiarmed Bandits
We present two alternative ways to apply PAC-Bayesian analysis to sequences
of dependent random variables. The first is based on a new lemma that enables
to bound expectations of convex functions of certain dependent random variables
by expectations of the same functions of independent Bernoulli random
variables. This lemma provides an alternative tool to Hoeffding-Azuma
inequality to bound concentration of martingale values. Our second approach is
based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis.
We also introduce a way to apply PAC-Bayesian analysis in situation of limited
feedback. We combine the new tools to derive PAC-Bayesian generalization and
regret bounds for the multiarmed bandit problem. Although our regret bound is
not yet as tight as state-of-the-art regret bounds based on other
well-established techniques, our results significantly expand the range of
potential applications of PAC-Bayesian analysis and introduce a new analysis
tool to reinforcement learning and many other fields, where martingales and
limited feedback are encountered
Boltzmann Exploration Done Right
Boltzmann exploration is a classic strategy for sequential decision-making
under uncertainty, and is one of the most standard tools in Reinforcement
Learning (RL). Despite its widespread use, there is virtually no theoretical
understanding about the limitations or the actual benefits of this exploration
scheme. Does it drive exploration in a meaningful way? Is it prone to
misidentifying the optimal actions or spending too much time exploring the
suboptimal ones? What is the right tuning for the learning rate? In this paper,
we address several of these questions in the classic setup of stochastic
multi-armed bandits. One of our main results is showing that the Boltzmann
exploration strategy with any monotone learning-rate sequence will induce
suboptimal behavior. As a remedy, we offer a simple non-monotone schedule that
guarantees near-optimal performance, albeit only when given prior access to key
problem parameters that are typically not available in practical situations
(like the time horizon and the suboptimality gap ). More
importantly, we propose a novel variant that uses different learning rates for
different arms, and achieves a distribution-dependent regret bound of order
and a distribution-independent bound of order
without requiring such prior knowledge. To demonstrate the
flexibility of our technique, we also propose a variant that guarantees the
same performance bounds even if the rewards are heavy-tailed
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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