At VMware research, I am involved in different projects spanning both applied and theoretical works in the domains of deep learning and generative AI. 

My postdoc work was mostly theoretical work that: 1) helps us better understand the empirical success of machine learning, and 2) helps us design better machine learning algorithms with theoretical guarantees.

Some of the projects I have worked on and/or I am still interested on working on are along the following topics:

• Parallel and multi-agent reinforcement learning (RL). How can multiple agents performing parallel exploration or learning in the same environment affect the accuracy or efficiency of RL algorithms? How can we leverage the experience or information collected by multiple agents in different (but not too distinct) environments, across multiple tasks?

• Deep learning. What theoretical insights and guarantees can we provide on the training of (deep and wide) neural networks in terms of the convergence properties of commonly used optimization algorithms and of random weight initialization? How do different hyperparameters and initializations schemes affect the interplay among training, generalization and robustness?

• Learning and game theoretic methods in robotics. How can learning aid robots in task planning or in motion planning (e.g., building guiding spaces, creating space representations, creating predictive behavior of obstacles)? Can we leverage game-theoretic frameworks to model multi-robot systems, even with humans in the loop? 

During my PhD studies, my research has been mainly on the areas of systems and control, particularly, on the areas of network systems or multi-agent systems and stability. Throughout my work, I have found applications where I have used concepts from  game theory, optimization theory and mathematical sociology. Some of my works on optimization are summarized in an abstract of a talk (link) I gave at UIUC (prior to my hiring!). 

The research projects have been, more specifically, along the following topics:

• Mathematical modeling of social processes. I have proposed and formally analyzed mathematical models that can express the dynamic evolution of different observed social phenomena, including the evolution of positive and negative interpersonal relationships over a social network, and opinion dynamics. I have studied the convergence of signed networks towards structural balance and clustering balance, as well as the polarization and fluctuation of opinions over different classes of social networks. I have used tools from dynamical systems and game theory.

• Stability tools with possible applications to multi-agent or network systems, and infinite-dimensional systems. I have studied a strong stability concept for dynamical systems called contraction theory - a framework which basically describes exponential incremental stability. I have used it to further characterize a solver of a class of constrained optimization problems called primal-dual dynamics, and extend it to both distributed and time-varying optimization cases. I have also extended contraction theory to Hilbert spaces, and collaborated on a work to extend weaker notions of contraction theory to different metrics and applications. 

• Epidemic models. I have formally analyzed and characterized a generalization of the network SIS epidemics model to the case of higher-order interactions, i.e., interactions that can be represented by hypergraphs.

• Estimation and graphical models. I have worked on the connection between the graphical lasso formulation and the framework of distributionally robust optimization.

• Wasserstein barycenters. I have a theoretical work that explores a way of computing Wasserstein barycenters - a concept related to optimal transport - through distributed pairwise computation over networks. 

I want to mention I love collaboration. Throughout my studies, I had multiple academic discussions - and even paper collaborations -  with faculty and post-docs from Sociology, Mechanical Engineering, Statistics, and Computer Science. 

My work has been theoretical and mathematically rigorous. I love finding problems where a theoretical approach is needed. However, having said that, I am always willing to (and would love to!) expand my work and collaboration to applied settings as well, where numerical simulations and physical experimentation is important, such as in robotics.

Other Interests and possible future work:

I am happy to continue working on different problems related to all the aforementioned research areas I have worked in the past. Other areas I would love to explore more about are computational economics (e.g., mechanism design,  auctions, etc.) and robotics (e.g., learning in robotics, embodied intelligence, smart motion planning, multi-robot systems, etc.). 

I also have a deep interest in difference areas of finance: in topics ranging from quantitative portfolio management, to trading of financial derivatives. I also have an interest in alternative investments such as cryptocurrencies - blockchain, DeFi, etc. - from both a theoretical and applied perspective, and study its effects as a disruptive technology.

Preprints:

• A. Attali, P. Cisneros-Velarde, M Morales and N. Amato, “Discrete State-Action Abstraction via the Successor Representation," 2022.

Published:

• P. Cisneros-Velarde, Sanmi Koyejo, "Finite-sample Guarantees for Nash Q-learning with Linear Function Approximation," Uncertainty in Artificial Intelligence (UAI), 2023.

• A Banerjee, P. Cisneros-Velarde, L. Zhu and M Belkin, “Neural tangent kernel at initialization: linear width suffices,” Uncertainty in Artificial Intelligence (UAI), 2023.

• A. Banerjee, P. Cisneros-Velarde, L. Zhu, M. Belkin, “Restricted Strong Convexity of Deep Learning Models with Smooth Activations," International Conference on Learning Representations (ICLR), 2023.

• P. Cisneros-Velarde, B. Lyu, S. Koyejo and M. Kolar, “One Policy is Enough: Parallel Exploration with a Single Policy is Near-Optimal for Reward-Free Reinforcement Learning," International Conference on Artificial Intelligence and Statistics (AISTATS), 2023.

• P. Cisneros-Velarde and F. Bullo, “Distributed Wasserstein Barycenters via Displacement Interpolation,” IEEE Transactions on Control  of Network Systems,  2022.

• P. Cisneros-Velarde and F. Bullo, “A Contraction Theory Approach to Optimization Algorithms from Acceleration Flows,” International Conference on Artificial Intelligence and Statistics (AISTATS), 2022.

• Francesco Bullo, Pedro Cisneros-Velarde, Alexander Davydov, Saber Jafarpour, "From contraction theory to fixed point algorithms on Riemannian and non-Euclidean spaces," 60th IEEE Conference on Decision and Control (CDC), 2021.

• P. Cisneros-Velarde, S. Jafarpour and F. Bullo, “Contraction Theory for Dynamical Systems on Hilbert Spaces,” IEEE Transactions on Automatic Control,  2021.

• P. Cisneros-Velarde and F. Bullo, “Multi-group SIS Epidemics with Simplicial and Higher-Order Interactions,” IEEE Transactions on Control  of Network Systems,  2021.

• P. Cisneros-Velarde, S. Jafarpour and F. Bullo, “Distributed and time-varying primal-dual dynamics via contraction analysis,” IEEE Transactions on Automatic Control, 2021.

• P. Cisneros-Velarde and F. Bullo, “A Network Formation Game for the Emergence of Hierarchies,” PloS One, 2021.

• S. Jafarpour, P. Cisneros-Velarde and F. Bullo, “Weak and Semi-Contraction Theory with Application to Network Systems,” IEEE Transactions on Automatic Control, 2021.

• P. Cisneros-Velarde, K. S. Chan, and F. Bullo, “Polarization and Fluctuations in Signed Social Networks,” IEEE Transactions on Automatic Control, 2020.

• P. Cisneros-Velarde, N. E. Friedkin, A. V. Proskurnikov, F. Bullo, ”Structural Balance via Gradient Flows over Signed Graphs,” IEEE Transactions on Automatic Control, 2020.

• P. Cisneros-Velarde, S. Y. Oh, and A. Petersen, “Distributionally Robust Formulation and Model Selection for the Graphical Lasso,” International Conference on Artificial Intelligence and Statistics (AISTATS), 2020.

• P. Cisneros-Velarde and F. Bullo, ”Signed Network Formation Games and Clustering Balance,” Dynamic Games and Applications, 2020.

• W. Mei, P. Cisneros-Velarde, G. Chen, N. E. Friedkin and F. Bullo, ”Dynamic social balance and convergent appraisals via homophily and influence mechanisms,” Automatica, 2019.

• P. Cisneros-Velarde, D. Oliveira, and K. Chan, ”Spread and Control of Misinformation with Heterogeneous Agents,” International Workshop on Complex Networks, 2019.