120 research outputs found
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
Discovering Valuable Items from Massive Data
Suppose there is a large collection of items, each with an associated cost
and an inherent utility that is revealed only once we commit to selecting it.
Given a budget on the cumulative cost of the selected items, how can we pick a
subset of maximal value? This task generalizes several important problems such
as multi-arm bandits, active search and the knapsack problem. We present an
algorithm, GP-Select, which utilizes prior knowledge about similarity be- tween
items, expressed as a kernel function. GP-Select uses Gaussian process
prediction to balance exploration (estimating the unknown value of items) and
exploitation (selecting items of high value). We extend GP-Select to be able to
discover sets that simultaneously have high utility and are diverse. Our
preference for diversity can be specified as an arbitrary monotone submodular
function that quantifies the diminishing returns obtained when selecting
similar items. Furthermore, we exploit the structure of the model updates to
achieve an order of magnitude (up to 40X) speedup in our experiments without
resorting to approximations. We provide strong guarantees on the performance of
GP-Select and apply it to three real-world case studies of industrial
relevance: (1) Refreshing a repository of prices in a Global Distribution
System for the travel industry, (2) Identifying diverse, binding-affine
peptides in a vaccine de- sign task and (3) Maximizing clicks in a web-scale
recommender system by recommending items to users
Distributed Online Learning via Cooperative Contextual Bandits
In this paper we propose a novel framework for decentralized, online learning
by many learners. At each moment of time, an instance characterized by a
certain context may arrive to each learner; based on the context, the learner
can select one of its own actions (which gives a reward and provides
information) or request assistance from another learner. In the latter case,
the requester pays a cost and receives the reward but the provider learns the
information. In our framework, learners are modeled as cooperative contextual
bandits. Each learner seeks to maximize the expected reward from its arrivals,
which involves trading off the reward received from its own actions, the
information learned from its own actions, the reward received from the actions
requested of others and the cost paid for these actions - taking into account
what it has learned about the value of assistance from each other learner. We
develop distributed online learning algorithms and provide analytic bounds to
compare the efficiency of these with algorithms with the complete knowledge
(oracle) benchmark (in which the expected reward of every action in every
context is known by every learner). Our estimates show that regret - the loss
incurred by the algorithm - is sublinear in time. Our theoretical framework can
be used in many practical applications including Big Data mining, event
detection in surveillance sensor networks and distributed online recommendation
systems
Learning in A Changing World: Restless Multi-Armed Bandit with Unknown Dynamics
We consider the restless multi-armed bandit (RMAB) problem with unknown
dynamics in which a player chooses M out of N arms to play at each time. The
reward state of each arm transits according to an unknown Markovian rule when
it is played and evolves according to an arbitrary unknown random process when
it is passive. The performance of an arm selection policy is measured by
regret, defined as the reward loss with respect to the case where the player
knows which M arms are the most rewarding and always plays the M best arms. We
construct a policy with an interleaving exploration and exploitation epoch
structure that achieves a regret with logarithmic order when arbitrary (but
nontrivial) bounds on certain system parameters are known. When no knowledge
about the system is available, we show that the proposed policy achieves a
regret arbitrarily close to the logarithmic order. We further extend the
problem to a decentralized setting where multiple distributed players share the
arms without information exchange. Under both an exogenous restless model and
an endogenous restless model, we show that a decentralized extension of the
proposed policy preserves the logarithmic regret order as in the centralized
setting. The results apply to adaptive learning in various dynamic systems and
communication networks, as well as financial investment.Comment: 33 pages, 5 figures, submitted to IEEE Transactions on Information
Theory, 201
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