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Raj Kumar Maity

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3 papers

2 author rows

NeurIPS Conference 2020 Conference Paper

Distributed Newton Can Communicate Less and Resist Byzantine Workers

Avishek Ghosh
Raj Kumar Maity
Arya Mazumdar

We develop a distributed second order optimization algorithm that is communication-efficient as well as robust against Byzantine failures of the worker machines. We propose an iterative approximate Newton-type algorithm, where the worker machines communicate \emph{only once} per iteration with the central machine. This is in sharp contrast with the state-of-the-art distributed second order algorithms like GIANT \cite{giant}, DINGO\cite{dingo}, where the worker machines send (functions of) local gradient and Hessian sequentially; thus ending up communicating twice with the central machine per iteration. Furthermore, we employ a simple norm based thresholding rule to filter-out the Byzantine worker machines. We establish the linear-quadratic rate of convergence of our proposed algorithm and establish that the communication savings and Byzantine resilience attributes only correspond to a small statistical error rate for arbitrary convex loss functions. To the best of our knowledge, this is the first work that addresses the issue of Byzantine resilience in second order distributed optimization. Furthermore, we validate our theoretical results with extensive experiments on synthetically generated and benchmark LIBSVM \cite{libsvm} data-set and demonstrate convergence guarantees.

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UAI Conference 2020 Conference Paper

High Dimensional Discrete Integration over the Hypergrid

Raj Kumar Maity
Arya Mazumdar
Soumyabrata Pal

Recently Ermon et al. (2013) pioneered a way to practically compute approximations to large scale counting or discrete integration problems by using random hashes. The hashes are used to reduce the counting problem into many separate discrete optimization problems. The optimization problems then can be solved by an NP-oracle such as commercial SAT solvers or integer linear programming (ILP) solvers. In particular, Ermon et al. showed that if the domain of integration is $\{0, 1\}^n$ then it is possible to obtain a solution within a factor of $16$ of the optimal (16-approximation) by this technique. In many crucial counting tasks, such as computation of partition function of ferromagnetic Potts model, the domain of integration is naturally $\{0, 1, …, q-1\}^n, q>2$, the hypergrid. The straightforward extension of Ermon et al. ’s method allows a $q^2$-approximation for this problem. For large values of $q$, this is undesirable. In this paper, we show an improved technique to obtain an approximation factor of $4+O(1/q^2)$ to this problem. We are able to achieve this by using an idea of optimization over multiple bins of the hash functions, that can be easily implemented by inequality constraints, or even in unconstrained way. The NP oracle in this setting can be simulated by using an ILP solver as in Ermon et. al. We provide simulation results to support the theoretical guarantees of our algorithms.

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ECAI Conference 2016 Conference Paper

Shaping Proto-Value Functions Using Rewards

Raj Kumar Maity
Chandra Shekar Lakshminarayanan
Sindhu Padakandla
Shalabh Bhatnagar

In reinforcement learning (RL), an important sub-problem is learning the value function, which is chiefly influenced by the architecture used to represent value functions. is often expressed as a linear combination of a pre-selected set of basis functions. These basis functions are either selected in an ad-hoc manner or are tailored to the RL task using the domain knowledge. Selecting basis functions in an ad-hoc manner does not give a good approximation of value function while choosing functions using domain knowledge introduces dependency on the task. Thus, a desirable scenario is to have a method to choose basis functions that are task independent, but which also provide a good approximation for the value function. In this paper, we propose a novel task-independent basis function construction method that uses the topology of the underlying state space and the reward structure to build the reward-based Proto Value Functions (RPVFs). The approach we propose gives good approximation for the value function and enhanced learning performance. The performance is demonstrated via experiments on grid-world tasks.

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