arXiv subjects

Ganesh Ghalme

Publications and source records attributed to Ganesh Ghalme.

23 records · Page 2Linked to original sources

arXiv2021

Sleeping Combinatorial Bandits

In this paper, we study an interesting combination of sleeping and combinatorial stochastic bandits. In the mixed model studied here, at each discrete time instant, an arbitrary \emph{availability set} is generated from a fixed set of \emph{base} arms. An algorithm can select a subset of arms from the \emph{availability set} (sleeping bandits) and receive the corresponding reward along with semi-bandit feedback (combinatorial bandits). We adapt the well-known CUCB algorithm in the sleeping combinatorial bandits setting and refer to it as \CSUCB. We prove -- under mild smoothness conditions -- that the \CSUCB\ algorithm achieves an $O(\log (T))$ instance-dependent regret guarantee. We further prove that (i) when the range of the rewards is bounded, the regret guarantee of \CSUCB\ algorithm is $O(\sqrt{T \log (T)})$ and (ii) the instance-independent regret is $O(\sqrt[3]{T^2 \log(T)})$ in a general setting. Our results are quite general and hold under general environments -- such as non-additive reward functions, volatile arm availability, a variable number of base-arms to be pulled -- arising in practical applications. We validate the proven theoretical guarantees through experiments.

cs.LG↗

arXiv2021

Ballooning Multi-Armed Bandits

In this paper, we introduce Ballooning Multi-Armed Bandits (BL-MAB), a novel extension of the classical stochastic MAB model. In the BL-MAB model, the set of available arms grows (or balloons) over time. In contrast to the classical MAB setting where the regret is computed with respect to the best arm overall, the regret in a BL-MAB setting is computed with respect to the best available arm at each time. We first observe that the existing stochastic MAB algorithms result in linear regret for the BL-MAB model. We prove that, if the best arm is equally likely to arrive at any time instant, a sub-linear regret cannot be achieved. Next, we show that if the best arm is more likely to arrive in the early rounds, one can achieve sub-linear regret. Our proposed algorithm determines (1) the fraction of the time horizon for which the newly arriving arms should be explored and (2) the sequence of arm pulls in the exploitation phase from among the explored arms. Making reasonable assumptions on the arrival distribution of the best arm in terms of the thinness of the distribution's tail, we prove that the proposed algorithm achieves sub-linear instance-independent regret. We further quantify explicit dependence of regret on the arrival distribution parameters. We reinforce our theoretical findings with extensive simulation results. We conclude by showing that our algorithm would achieve sub-linear regret even if (a) the distributional parameters are not exactly known, but are obtained using a reasonable learning mechanism or (b) the best arm is not more likely to arrive early, but a large fraction of arms is likely to arrive relatively early.

cs.LG↗

arXiv2020

Achieving Fairness in the Stochastic Multi-armed Bandit Problem

We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called $r$-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two parameters: the unfairness tolerance and the learning algorithm used as a black-box. We provide a fairness guarantee for this class that holds uniformly over time irrespective of the choice of the learning algorithm. In particular, when the learning algorithm is UCB1, we show that our algorithm achieves $O(\ln T)$ $r$-Regret. Finally, we evaluate the cost of fairness in terms of the conventional notion of regret.

cs.LG↗

arXiv2019

Achieving Fairness in Stochastic Multi-armed Bandit Problem

We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called r-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two parameters: the unfairness tolerance and learning algorithm used as a black-box. We provide a fairness guarantee for this class that holds uniformly over time irrespective of the choice of the learning algorithm. In particular, when the learning algorithm is UCB1, we show that our algorithm achieves O(log(T)) r-Regret. Finally, we evaluate the cost of fairness in terms of the conventional notion of regret.

cs.LG↗

arXiv2019

Fair Division of Indivisible Goods Among Strategic Agents

We study fair division of indivisible goods in a single-parameter environment. In particular, we develop truthful social welfare maximizing mechanisms for fairly allocating indivisible goods. Our fairness guarantees are in terms of solution concepts which are tailored to address allocation of indivisible goods and, hence, provide an appropriate framework for fair division of goods. This work specifically considers fairness in terms of envy freeness up to one good (EF1), maximin share guarantee (MMS), and Nash social welfare (NSW). Our first result shows that (in a single-parameter environment) the problem of maximizing welfare, subject to the constraint that the allocation of the indivisible goods is EF1, admits a polynomial-time, 1/2-approximate, truthful auction. We further prove that this problem is NP-Hard and, hence, an approximation is warranted. This hardness result also complements prior works which show that an arbitrary EF1 allocation can be computed efficiently. We also establish a bi-criteria approximation guarantee for the problem of maximizing social welfare under MMS constraints. In particular, we develop a truthful auction which efficiently finds an allocation wherein each agent gets a bundle of value at least $\left(1/2 - \varepsilon \right)$ times her maximin share and the welfare of the computed allocation is at least the optimal, here $\varepsilon >0$ is a fixed constant. We complement this result by showing that maximizing welfare is computationally hard even if one aims to only satisfy the MMS constraint approximately.

cs.GT↗