698 research outputs found
Dynamic Ad Allocation: Bandits with Budgets
We consider an application of multi-armed bandits to internet advertising
(specifically, to dynamic ad allocation in the pay-per-click model, with
uncertainty on the click probabilities). We focus on an important practical
issue that advertisers are constrained in how much money they can spend on
their ad campaigns. This issue has not been considered in the prior work on
bandit-based approaches for ad allocation, to the best of our knowledge.
We define a simple, stylized model where an algorithm picks one ad to display
in each round, and each ad has a \emph{budget}: the maximal amount of money
that can be spent on this ad. This model admits a natural variant of UCB1, a
well-known algorithm for multi-armed bandits with stochastic rewards. We derive
strong provable guarantees for this algorithm
One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits
We address the problem of \emph{`Internal Regret'} in \emph{Sleeping Bandits}
in the fully adversarial setup, as well as draw connections between different
existing notions of sleeping regrets in the multiarmed bandits (MAB) literature
and consequently analyze the implications: Our first contribution is to propose
the new notion of \emph{Internal Regret} for sleeping MAB. We then proposed an
algorithm that yields sublinear regret in that measure, even for a completely
adversarial sequence of losses and availabilities. We further show that a low
sleeping internal regret always implies a low external regret, and as well as a
low policy regret for iid sequence of losses. The main contribution of this
work precisely lies in unifying different notions of existing regret in
sleeping bandits and understand the implication of one to another. Finally, we
also extend our results to the setting of \emph{Dueling Bandits} (DB)--a
preference feedback variant of MAB, and proposed a reduction to MAB idea to
design a low regret algorithm for sleeping dueling bandits with stochastic
preferences and adversarial availabilities. The efficacy of our algorithms is
justified through empirical evaluations
Online Learning for Changing Environments using Coin Betting
A key challenge in online learning is that classical algorithms can be slow
to adapt to changing environments. Recent studies have proposed "meta"
algorithms that convert any online learning algorithm to one that is adaptive
to changing environments, where the adaptivity is analyzed in a quantity called
the strongly-adaptive regret. This paper describes a new meta algorithm that
has a strongly-adaptive regret bound that is a factor of
better than other algorithms with the same time complexity, where is the
time horizon. We also extend our algorithm to achieve a first-order (i.e.,
dependent on the observed losses) strongly-adaptive regret bound for the first
time, to our knowledge. At its heart is a new parameter-free algorithm for the
learning with expert advice (LEA) problem in which experts sometimes do not
output advice for consecutive time steps (i.e., \emph{sleeping} experts). This
algorithm is derived by a reduction from optimal algorithms for the so-called
coin betting problem. Empirical results show that our algorithm outperforms
state-of-the-art methods in both learning with expert advice and metric
learning scenarios.Comment: submitted to a journal. arXiv admin note: substantial text overlap
with arXiv:1610.0457
Dueling Bandits with Adversarial Sleeping
We introduce the problem of sleeping dueling bandits with stochastic
preferences and adversarial availabilities (DB-SPAA). In almost all dueling
bandit applications, the decision space often changes over time; eg, retail
store management, online shopping, restaurant recommendation, search engine
optimization, etc. Surprisingly, this `sleeping aspect' of dueling bandits has
never been studied in the literature. Like dueling bandits, the goal is to
compete with the best arm by sequentially querying the preference feedback of
item pairs. The non-triviality however results due to the non-stationary item
spaces that allow any arbitrary subsets items to go unavailable every round.
The goal is to find an optimal `no-regret' policy that can identify the best
available item at each round, as opposed to the standard `fixed best-arm regret
objective' of dueling bandits. We first derive an instance-specific lower bound
for DB-SPAA , where is the number of items and is the
gap between items and . This indicates that the sleeping problem with
preference feedback is inherently more difficult than that for classical
multi-armed bandits (MAB). We then propose two algorithms, with near optimal
regret guarantees. Our results are corroborated empirically
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