P. Kiran Kumar Reddy

Danial Dervovic, Parisa Hassanzadeh, Samuel Assefa et al.

We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the constraint that they may only accept at most $n$ jobs over some reference time period. The decision-maker only has access to $M$ independent realisations of the job arrival process. We propose an algorithm, Non-Parametric Sequential Allocation (NPSA), for solving this problem. Moreover, we prove that the expected reward returned by the NPSA algorithm converges in probability to optimality as $M$ grows large. We demonstrate the effectiveness of the algorithm empirically on synthetic data and on public fraud-detection datasets, from where the motivation for this work is derived.

Nelson Vadori, Sumitra Ganesh, Prashant Reddy et al.

We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the cumulative reward as a whole, we aim at learning policies sensitive to the uncertain/stochastic nature of the rewards, which has the advantage of being conceptually more meaningful in some cases. To this end, we present a new decomposition of the randomness contained in the cumulative reward based on the Doob decomposition of a stochastic process, and introduce a new conceptual tool - the \textit{chaotic variation} - which can rigorously be interpreted as the risk measure of the martingale component associated to the cumulative reward process. We innovate on the reinforcement learning side by incorporating this new risk-sensitive approach into model-free algorithms, both policy gradient and value function based, and illustrate its relevance on grid world and portfolio optimization problems.