1. Sequential Decision Making (MDP, POMDP)
Markov Decision Processes (MDPs) and Partially Observable Markov Decision Processes (POMDPs) provide a flexible mathematical framework for modeling decision making when uncertainty is present in the system. My research primarily focuses on solving MDPs and POMDPs with continuous action and observation spaces, such that the proposed algorithms not only have provable theoretical convergence guarantees but also are computationally efficient and can be deployed in real autonomous systems.
- Sparse tree search optimality guarantees in POMDPs with continuous observation spaces.
Lim, M. H., Tomlin, C. J., & Sunberg, Z. N. (2019). IJCAI-PRICAI 2020 (Under Review). [arXiv]
2. Learning-Based Perception with Model-Based Control
In many realistic scenarios, simple and well-understood dynamics models are sufficient for control, such as navigation for model cars or quadcopters. Rather, the burden is on the vision and perception components that require learning. My research focuses on efficiently combining deep-learning based perception with optimal control models, such that the agents can navigate in a priori unknown environments.
- Quadcopter 3D Visual Waypoint Navigation.
In this line of work, we focus on implementing and extending the Visual Waypoint Navigation to quadcopters, such that the agent is able to navigate in unknown 3D environments.
IMC Financial Markets (Jan. 2016 - Aug. 2016)
As a summer intern, I modeled inter-index and inter-expiry implied volatility correlations through on-line updates with weighted linear regression. With the model, I proposed a correction to the pricing model to factor in implied vol. correlations to improve estimated trading gains up to $1,000/day.
As a winter intern, I learned theoretical and technical concepts of quantitative trading, such as valuation and quote allocation, through mock trading and mini programming projects using Python's pandas library.
Stochastic MCMC Simulation
Harvard University - Advisor: Prof. Samuel Kou (2016 - 2018)
Computational Condensed Matter
Georgetown University Physics REU - Advisor: Prof. James Freericks (2015)
- Creating analogs of thermal distributions from diabatic excitations in ion-trap-based quantum simulation.
Lim, M. H., Yoshimura, B. T., & Freericks, J. K. (2016). New J. Phys. 18 043026. [pdf] [arXiv]
Harvard University - Advisor: Prof. James Freericks (2015)
Geometric Graph Theory
Indiana University, Hofstra University - Advisor: Prof. Geoffrey Exoo, Prof. Dan Ismailescu (2012 - 2014)
- On the Chromatic Number of R4.
Exoo, G., Ismailescu, D., & Lim, M. (2014). Disc. Comput. Geom. 52(2): 416. [pdf]