Ranveer Singh

Priyanshu Pant, Ranveer Singh

Galluccio--Loebl and Tesler showed that the perfect-matching polynomial of a graph embedded in an orientable surface of genus $g$ can be written as a linear combination of at most $4^g$ Pfaffians. We show that, in general, exponentially many Pfaffians are necessary. More precisely, among all graphs of orientable genus at most $g$, the maximum possible Pfaffian number is at least $(8/3)^g$. This lower bound holds even for connected matching-covered graphs. We also obtain exponential lower bounds for the Pfaffian number of complete bipartite graphs, and hence for even complete graphs, improving asymptotically on a recent linear lower bound of Junchaya, Lucchesi, and Miranda.

Yiyang Lu, Haresh Jadav, Mohammad Pedramfar et al.

We study online maximization of non-monotone Diminishing-Return(DR)-submodular functions over down-closed convex sets, a regime where existing projection-free online methods suffer from suboptimal regret and limited feedback guarantees. Our main contribution is a new structural result showing that this class is $1/e$-linearizable under carefully designed exponential reparametrization, scaling parameter, and surrogate potential, enabling a reduction to online linear optimization. As a result, we obtain $O(T^{1/2})$ static regret with a single gradient query per round and unlock adaptive and dynamic regret guarantees, together with improved rates under semi-bandit, bandit, and zeroth-order feedback. Across all feedback models, our bounds strictly improve the state of the art.

Hareshkumar Jadav, Ranveer Singh, Vaneet Aggarwal

Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $γ$-weakly DR-submodular function over a down-closed convex body. Our main result is an approximation algorithm whose guarantee depends smoothly on $γ$; in particular, when $γ=1$ (the DR-submodular case) our bound recovers the $0.401$ approximation factor, while for $γ<1$ the guarantee degrades gracefully and, it improves upon previously reported bounds for $γ$-weakly DR-submodular maximization under the same constraints. Our approach combines a Frank-Wolfe-guided continuous-greedy framework with a $γ$-aware double-greedy step, yielding a simple yet effective procedure for handling non-monotonicity. This results in state-of-the-art guarantees for non-monotone $γ$-weakly DR-submodular maximization over down-closed convex bodies.

Priyanshu Pant, Ranveer Singh

For a simple graph $G$ with adjacency matrix $A(G)$, let $π(G,x):=\mathrm{per}(xI-A(G))$ be its permanental polynomial with roots $μ_1,\ldots,μ_n \in \mathbb{C}$, and define the permanental energy $E_{\mathrm{per}}(G):=\sum_{i=1}^n |μ_i|$. We prove a sharp universal lower bound: for every $m$-edge graph $G$, $E_{\mathrm{per}}(G) \ge 2\sqrt{m}$, with equality if and only if $G$ is a star together with isolated vertices. We also prove the general upper bound $E_{\mathrm{per}}(G) \le nρ(G)$, where $ρ(G)$ is the spectral radius, and we study $E_{\mathrm{per}}(G)$ on several graph families.

Priyanshu Pant, Ranveer Singh

In 1982, Chollet conjectured that $\mathrm{per}(A\circ B)\le \mathrm{per}(A)\mathrm{per}(B)$ for Hermitian positive semidefinite matrices $A,B$, where $\circ$ denotes the Hadamard product, and observed that in the real symmetric case it suffices to prove $\mathrm{per}(A\circ A)\le \mathrm{per}(A)^2$. We prove $\mathrm{per}(A\circ A)\le \mathrm{per}(A)^2$ for symmetric $Z$-matrices with nonnegative diagonal whose support graph is bipartite. Motivated by this, we study the Laplacian inequality $\mathrm{per}(L_G\circ L_G)\le \mathrm{per}(L_G)^2$ for the graph Laplacian $L_G$. We introduce a compositional framework for permanental inequalities on graph Laplacians, showing that Chollet's inequality is preserved under vertex coalescence. This enables the extension of the inequality from basic graph classes to large structured families, revealing new tractable regimes for a fundamentally $\#P$-hard quantity.

Nikhilesh Prabhakar, Ranveer Singh, Harsha Kokel et al. · ibm-research

Multiagent Reinforcement Learning (MARL) poses significant challenges due to the exponential growth of state and action spaces and the non-stationary nature of multiagent environments. This results in notable sample inefficiency and hinders generalization across diverse tasks. The complexity is further pronounced in relational settings, where domain knowledge is crucial but often underutilized by existing MARL algorithms. To overcome these hurdles, we propose integrating relational planners as centralized controllers with efficient state abstractions and reinforcement learning. This approach proves to be sample-efficient and facilitates effective task transfer and generalization.

Ranveer Singh, Bidyut Kr. Patra, Bibhas Adhikari

Collaborative filtering (CF) is the most widely used and successful approach for personalized service recommendations. Among the collaborative recommendation approaches, neighborhood based approaches enjoy a huge amount of popularity, due to their simplicity, justifiability, efficiency and stability. Neighborhood based collaborative filtering approach finds K nearest neighbors to an active user or K most similar rated items to the target item for recommendation. Traditional similarity measures use ratings of co-rated items to find similarity between a pair of users. Therefore, traditional similarity measures cannot compute effective neighbors in sparse dataset. In this paper, we propose a two-phase approach, which generates user-user and item-item networks using traditional similarity measures in the first phase. In the second phase, two hybrid approaches HB1, HB2, which utilize structural similarity of both the network for finding K nearest neighbors and K most similar items to a target items are introduced. To show effectiveness of the measures, we compared performances of neighborhood based CFs using state-of-the-art similarity measures with our proposed structural similarity measures based CFs. Recommendation results on a set of real data show that proposed measures based CFs outperform existing measures based CFs in various evaluation metrics.