1,556 research outputs found
Combinatorial Network Optimization with Unknown Variables: Multi-Armed Bandits with Linear Rewards
In the classic multi-armed bandits problem, the goal is to have a policy for
dynamically operating arms that each yield stochastic rewards with unknown
means. The key metric of interest is regret, defined as the gap between the
expected total reward accumulated by an omniscient player that knows the reward
means for each arm, and the expected total reward accumulated by the given
policy. The policies presented in prior work have storage, computation and
regret all growing linearly with the number of arms, which is not scalable when
the number of arms is large. We consider in this work a broad class of
multi-armed bandits with dependent arms that yield rewards as a linear
combination of a set of unknown parameters. For this general framework, we
present efficient policies that are shown to achieve regret that grows
logarithmically with time, and polynomially in the number of unknown parameters
(even though the number of dependent arms may grow exponentially). Furthermore,
these policies only require storage that grows linearly in the number of
unknown parameters. We show that this generalization is broadly applicable and
useful for many interesting tasks in networks that can be formulated as
tractable combinatorial optimization problems with linear objective functions,
such as maximum weight matching, shortest path, and minimum spanning tree
computations
Context Attentive Bandits: Contextual Bandit with Restricted Context
We consider a novel formulation of the multi-armed bandit model, which we
call the contextual bandit with restricted context, where only a limited number
of features can be accessed by the learner at every iteration. This novel
formulation is motivated by different online problems arising in clinical
trials, recommender systems and attention modeling. Herein, we adapt the
standard multi-armed bandit algorithm known as Thompson Sampling to take
advantage of our restricted context setting, and propose two novel algorithms,
called the Thompson Sampling with Restricted Context(TSRC) and the Windows
Thompson Sampling with Restricted Context(WTSRC), for handling stationary and
nonstationary environments, respectively. Our empirical results demonstrate
advantages of the proposed approaches on several real-life datasetsComment: IJCAI 201
Deterministic Sequencing of Exploration and Exploitation for Multi-Armed Bandit Problems
In the Multi-Armed Bandit (MAB) problem, there is a given set of arms with
unknown reward models. At each time, a player selects one arm to play, aiming
to maximize the total expected reward over a horizon of length T. An approach
based on a Deterministic Sequencing of Exploration and Exploitation (DSEE) is
developed for constructing sequential arm selection policies. It is shown that
for all light-tailed reward distributions, DSEE achieves the optimal
logarithmic order of the regret, where regret is defined as the total expected
reward loss against the ideal case with known reward models. For heavy-tailed
reward distributions, DSEE achieves O(T^1/p) regret when the moments of the
reward distributions exist up to the pth order for 1<p<=2 and O(T^1/(1+p/2))
for p>2. With the knowledge of an upperbound on a finite moment of the
heavy-tailed reward distributions, DSEE offers the optimal logarithmic regret
order. The proposed DSEE approach complements existing work on MAB by providing
corresponding results for general reward distributions. Furthermore, with a
clearly defined tunable parameter-the cardinality of the exploration sequence,
the DSEE approach is easily extendable to variations of MAB, including MAB with
various objectives, decentralized MAB with multiple players and incomplete
reward observations under collisions, MAB with unknown Markov dynamics, and
combinatorial MAB with dependent arms that often arise in network optimization
problems such as the shortest path, the minimum spanning, and the dominating
set problems under unknown random weights.Comment: 22 pages, 2 figure
- …