arXiv subjects

Girish Raguvir J

Publications and source records attributed to Girish Raguvir J.

3 recordsLinked to original sources

arXiv2020

Dynamic Data Structures for Interval Coloring

We consider the dynamic graph coloring problem restricted to the class of interval graphs. At each update step the algorithm is presented with an interval to be colored, or a previously colored interval to delete. The goal of the algorithm is to efficiently maintain a proper coloring of the intervals with as few colors as possible by an online algorithm. In the incremental model, each update step presents the algorithm with an interval to be colored. The problem is closely connected to the online vertex coloring problem of interval graphs for which the Kierstead-Trotter (KT) algorithm achieves the best possible competitive ratio. We first show that a sub-quadratic time direct implementation of the KT-algorithm is unlikely to exist conditioned on the correctness of the Online Boolean Matrix Vector multiplication conjecture due to Henzinger et al. \cite{DBLP:conf/stoc/HenzingerKNS15}. We then design an incremental algorithm that is subtly different from the KT-algorithm and uses at most $3 ω- 2$ colors, where $ω$ is the maximum clique in the interval graph associated with the set of intervals. Our incremental data structure maintains a proper coloring in amortized $O(\log n + Δ)$ update time where $n$ is the total number of intervals inserted and $Δ$ is the maximum degree of a vertex in the interval graph. We then consider the fully dynamic framework involving insertions and deletions. On each update, our aim is to maintain a $3 ω- 2$ coloring of the remaining set of intervals, where $ω$ is the maximum clique in the interval graph associated with the remaining set of intervals. Our fully dynamic algorithm supports insertion of an interval in $O(\log n + Δ\log ω)$ worst case update time and deletion of an interval in $O(Δ^2 \log n)$ worst case update time.

cs.DS↗

arXiv2017

AUPCR Maximizing Matchings : Towards a Pragmatic Notion of Optimality for One-Sided Preference Matchings

We consider the problem of computing a matching in a bipartite graph in the presence of one-sided preferences. There are several well studied notions of optimality which include pareto optimality, rank maximality, fairness and popularity. In this paper, we conduct an in-depth experimental study comparing different notions of optimality based on a variety of metrics like cardinality, number of rank-1 edges, popularity, to name a few. Observing certain shortcomings in the standard notions of optimality, we propose an algorithm which maximizes an alternative metric called the Area under Profile Curve ratio (AUPCR). To the best of our knowledge, the AUPCR metric was used earlier but there is no known algorithm to compute an AUPCR maximizing matching. Finally, we illustrate the superiority of the AUPCR-maximizing matching by comparing its performance against other optimal matchings on synthetic instances modeling real-world data.

cs.MA↗

arXiv2017

Learning to Mix n-Step Returns: Generalizing lambda-Returns for Deep Reinforcement Learning

Reinforcement Learning (RL) can model complex behavior policies for goal-directed sequential decision making tasks. A hallmark of RL algorithms is Temporal Difference (TD) learning: value function for the current state is moved towards a bootstrapped target that is estimated using next state's value function. $λ$-returns generalize beyond 1-step returns and strike a balance between Monte Carlo and TD learning methods. While lambda-returns have been extensively studied in RL, they haven't been explored a lot in Deep RL. This paper's first contribution is an exhaustive benchmarking of lambda-returns. Although mathematically tractable, the use of exponentially decaying weighting of n-step returns based targets in lambda-returns is a rather ad-hoc design choice. Our second major contribution is that we propose a generalization of lambda-returns called Confidence-based Autodidactic Returns (CAR), wherein the RL agent learns the weighting of the n-step returns in an end-to-end manner. This allows the agent to learn to decide how much it wants to weigh the n-step returns based targets. In contrast, lambda-returns restrict RL agents to use an exponentially decaying weighting scheme. Autodidactic returns can be used for improving any RL algorithm which uses TD learning. We empirically demonstrate that using sophisticated weighted mixtures of multi-step returns (like CAR and lambda-returns) considerably outperforms the use of n-step returns. We perform our experiments on the Asynchronous Advantage Actor Critic (A3C) algorithm in the Atari 2600 domain.

cs.LG↗