Naman Agarwal

Learn More
We consider the problem of identifying underlying community-like structures in graphs. Towards this end we study the Stochastic Block Model (SBM) on k-clusters: a random model on n = km vertices, partitioned in k equal sized clusters, with edges sampled independently across clusters with probability q and within clusters with probability p, p > q. The goal(More)
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we develop second-order stochastic methods(More)
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which is linear in the input representation. The previously fastest methods run in time proportional to matrix inversion or worse. The time complexity of our algorithm to find a local minimum is even faster than that of gradient(More)
We give a simple necessary and sufficient condition for the dynamical equivalence of two coupled cell networks with different network architectures. The results are applicable to both continuous and discrete dynamical systems and are framed in terms of what we term input and output equivalence. We also give an algorithm that allows explicit construction of(More)
A k-lift of an n-vertex base-graph G is a graph H on n × k vertices, where each vertex of G is replaced by k vertices and each edge (u, v) in G is replaced by a matching representing a bijection π uv so that the edges of H are of the form (u, i), (v, π uv (i)). H is a (uniformly) random lift of G if for every edge (u, v) the bijection π uv is chosen(More)
We show that two networks of coupled dynamical systems are dynamically equivalent if and only if they are output equivalent. We also obtain necessary and sufficient conditions for two dynamically equivalent networks to be input equivalent. These results were previously described in the companion paper 'Dynami-cal equivalence of networks of coupled dynamical(More)
We design differentially private algorithms for the problem of online linear optimization in the full information and bandit settings with optimal˜O(√ T) 1 regret bounds. In the full-information setting, our results demonstrate that (ε, δ)-differential privacy may be ensured for free – in particular, the regret bounds scale as O(√ T) + ˜ O 1 ε log 1 δ. For(More)
In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the Goemans-Williamson semidefinite program (SDP) for Max-2-LIN(Z 2). We conjecture that adding triangle inequalities to the SDP provides a polynomial time(More)