485 research outputs found
Functional Bandits
We introduce the functional bandit problem, where the objective is to find an
arm that optimises a known functional of the unknown arm-reward distributions.
These problems arise in many settings such as maximum entropy methods in
natural language processing, and risk-averse decision-making, but current
best-arm identification techniques fail in these domains. We propose a new
approach, that combines functional estimation and arm elimination, to tackle
this problem. This method achieves provably efficient performance guarantees.
In addition, we illustrate this method on a number of important functionals in
risk management and information theory, and refine our generic theoretical
results in those cases
Finding a most biased coin with fewest flips
We study the problem of learning a most biased coin among a set of coins by
tossing the coins adaptively. The goal is to minimize the number of tosses
until we identify a coin i* whose posterior probability of being most biased is
at least 1-delta for a given delta. Under a particular probabilistic model, we
give an optimal algorithm, i.e., an algorithm that minimizes the expected
number of future tosses. The problem is closely related to finding the best arm
in the multi-armed bandit problem using adaptive strategies. Our algorithm
employs an optimal adaptive strategy -- a strategy that performs the best
possible action at each step after observing the outcomes of all previous coin
tosses. Consequently, our algorithm is also optimal for any starting history of
outcomes. To our knowledge, this is the first algorithm that employs an optimal
adaptive strategy under a Bayesian setting for this problem. Our proof of
optimality employs tools from the field of Markov games
Online Regret Bounds for Undiscounted Continuous Reinforcement Learning
We derive sublinear regret bounds for undiscounted reinforcement learning in
continuous state space. The proposed algorithm combines state aggregation with
the use of upper confidence bounds for implementing optimism in the face of
uncertainty. Beside the existence of an optimal policy which satisfies the
Poisson equation, the only assumptions made are Holder continuity of rewards
and transition probabilities
An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits
In this paper, we propose an information-theoretic exploration strategy for
stochastic, discrete multi-armed bandits that achieves optimal regret. Our
strategy is based on the value of information criterion. This criterion
measures the trade-off between policy information and obtainable rewards. High
amounts of policy information are associated with exploration-dominant searches
of the space and yield high rewards. Low amounts of policy information favor
the exploitation of existing knowledge. Information, in this criterion, is
quantified by a parameter that can be varied during search. We demonstrate that
a simulated-annealing-like update of this parameter, with a sufficiently fast
cooling schedule, leads to an optimal regret that is logarithmic with respect
to the number of episodes.Comment: Entrop
Satisficing in multi-armed bandit problems
Satisficing is a relaxation of maximizing and allows for less risky decision
making in the face of uncertainty. We propose two sets of satisficing
objectives for the multi-armed bandit problem, where the objective is to
achieve reward-based decision-making performance above a given threshold. We
show that these new problems are equivalent to various standard multi-armed
bandit problems with maximizing objectives and use the equivalence to find
bounds on performance. The different objectives can result in qualitatively
different behavior; for example, agents explore their options continually in
one case and only a finite number of times in another. For the case of Gaussian
rewards we show an additional equivalence between the two sets of satisficing
objectives that allows algorithms developed for one set to be applied to the
other. We then develop variants of the Upper Credible Limit (UCL) algorithm
that solve the problems with satisficing objectives and show that these
modified UCL algorithms achieve efficient satisficing performance.Comment: To appear in IEEE Transactions on Automatic Contro
- …