338 research outputs found
Decentralized Learning for Multi-player Multi-armed Bandits
We consider the problem of distributed online learning with multiple players
in multi-armed bandits (MAB) models. Each player can pick among multiple arms.
When a player picks an arm, it gets a reward. We consider both i.i.d. reward
model and Markovian reward model. In the i.i.d. model each arm is modelled as
an i.i.d. process with an unknown distribution with an unknown mean. In the
Markovian model, each arm is modelled as a finite, irreducible, aperiodic and
reversible Markov chain with an unknown probability transition matrix and
stationary distribution. The arms give different rewards to different players.
If two players pick the same arm, there is a "collision", and neither of them
get any reward. There is no dedicated control channel for coordination or
communication among the players. Any other communication between the users is
costly and will add to the regret. We propose an online index-based distributed
learning policy called algorithm that trades off
\textit{exploration v. exploitation} in the right way, and achieves expected
regret that grows at most as near-. The motivation comes from
opportunistic spectrum access by multiple secondary users in cognitive radio
networks wherein they must pick among various wireless channels that look
different to different users. This is the first distributed learning algorithm
for multi-player MABs to the best of our knowledge.Comment: 33 pages, 3 figures. Submitted to IEEE Transactions on Information
Theor
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
An Online Approach to Dynamic Channel Access and Transmission Scheduling
Making judicious channel access and transmission scheduling decisions is
essential for improving performance as well as energy and spectral efficiency
in multichannel wireless systems. This problem has been a subject of extensive
study in the past decade, and the resulting dynamic and opportunistic channel
access schemes can bring potentially significant improvement over traditional
schemes. However, a common and severe limitation of these dynamic schemes is
that they almost always require some form of a priori knowledge of the channel
statistics. A natural remedy is a learning framework, which has also been
extensively studied in the same context, but a typical learning algorithm in
this literature seeks only the best static policy, with performance measured by
weak regret, rather than learning a good dynamic channel access policy. There
is thus a clear disconnect between what an optimal channel access policy can
achieve with known channel statistics that actively exploits temporal, spatial
and spectral diversity, and what a typical existing learning algorithm aims
for, which is the static use of a single channel devoid of diversity gain. In
this paper we bridge this gap by designing learning algorithms that track known
optimal or sub-optimal dynamic channel access and transmission scheduling
policies, thereby yielding performance measured by a form of strong regret, the
accumulated difference between the reward returned by an optimal solution when
a priori information is available and that by our online algorithm. We do so in
the context of two specific algorithms that appeared in [1] and [2],
respectively, the former for a multiuser single-channel setting and the latter
for a single-user multichannel setting. In both cases we show that our
algorithms achieve sub-linear regret uniform in time and outperforms the
standard weak-regret learning algorithms.Comment: 10 pages, to appear in MobiHoc 201
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