About Me

Mini-Biography

I completed my bachelor of science (2010 - 2015), master of science (2015 - 2017) and doctor of philosophy (2017 - 2022) at the St. George campus of University of Toronto. All my degrees are in electrical and computer engineering). 

I am someone who is interested in all aspects of technology, particularly those that mesh well with high-powered mathematical analysis. During my undergrad I have performed various research projects in the field of power engineering, robotics, biomedical signal processing. My interest eventually carried me to systems control engineering, a field broad enough to allow me to explore whatever happens to piques my interest. 

My research lies at the intersection between game theory, machine learning and control theory and their applications. More specifically, I have been interested in:

• optimal control and differential games (multiplayer optimal control),

• accelerated optimization on non-Euclidean manifolds,

• all areas of machine learning and its interface with game theory,

• online learning and bandit algorithms for games,   

• MDP-based reinforcement learning and inverse reinforcement learning,

• generative adversarial networks and generative adversarial imitation learning,

• computational social science/sociology/psychological/behavioral science.

The research I feel most passionate about is applying computational techniques to analyze people and society. I see my past work in game theory as a foray into my long term vision, which is to algorthmatize research from the "soft sciences" and develop technology that can aid people in health, therapy, social work, and better society. 

PUBLICATIONS

Journal

• B. Gao and L. Pavel, “Second-Order Mirror Descent: Convergence in Games Beyond Averaging and Discounting,” arXiv preprint, arXiv:2111.09982v3, 2023 (conditionally accepted by IEEE TAC).

• B. Gao and L. Pavel, "Continuous-Time Discounted Mirror Descent Dynamics in Monotone Concave Games," in IEEE Transactions on Automatic Control, vol. 66, no. 11, pp. 5451-5458, Nov. 2021

• B. Gao and L. Pavel. “Continuous-Time Convergence Rates in Potential and Monotone Games,” SIAM Journal on Control and Optimization, 2022.

• B. Gao and L. Pavel, "On Passivity, Reinforcement Learning, and Higher Order Learning in Multiagent Finite Games," in IEEE Transactions on Automatic Control, vol. 66, no. 1, pp. 121-136, Jan. 2021.

IEEE Transactions on Automatic Control (TAC) consists of high-quality papers on the theory, design, and applications of control engineering 

SIAM Journal on Control and Optimization (SICON) contains research articles on the mathematics and applications of control theory and on those parts of optimization theory concerned with the dynamics of deterministic or stochastic systems in continuous or discrete time or otherwise dealing with differential equations, dynamics, infinite-dimensional spaces, or fundamental issues in variational analysis and geometry.

Conference

• B. Gao and L. Pavel, "Bandit learning with regularized second-order mirror descent," 2022 IEEE 61st Conference on Decision and Control (CDC), Cancun, Mexico, 2022.

• B. Gao and L. Pavel, "Second-order mirror descent: exact convergence beyond strictly stable equilibria in concave games," 2021 60th IEEE Conference on Decision and Control (CDC), Austin, TX, USA, 2021.

• B. Gao and L. Pavel, "On the Rate of Convergence of Continuous-Time Game Dynamics in N-Player Potential Games”, in Proc. IEEE Conference on Decision and Control (CDC), Jeju, South Korea, pp. 1678-1683, 2020.

• B. Gao and L. Pavel, "Discounted Mirror Descent Dynamics in Concave Games," 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France, 2019, pp. 5942-5947.

• B. Gao and L. Pavel, "On Passivity and Reinforcement Learning in Finite Games," 2018 IEEE Conference on Decision and Control (CDC), Miami, FL, USA, 2018, pp. 340-345.

IEEE Control and Decision Conference (CDC) is recognized as the premier scientific and engineering conference dedicated to the advancement of the theory and practice of systems and control.  

Preprint

B. Gao and L. Pavel, “On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning”, arXiv:1704.00805 [math], Apr. 2017.

TEACHING EXPERIENCE

As a teaching assistant

Machine Learning, Artificial Intelligence, AI

• APS1070 Foundations of Data Analytics and Machine Learning 

• APS360 Introduction to Artificial Intelligence

• CSC2516 Neural Networks and Deep Learning

• ECE421 Introduction to Machine Learning (UofT ECE Best TA Award 2021)

• ECE1513 Introduction to Machine Learning 

Optimization and Control 

• CSC2305 Numerical Methods for Optimization Problems 

• ECE557 Linear Control Theory 

• ECE411 Discrete-Time Control 

• ECE311 Dynamical System and Control

Communication engineering and signal processing

• ECE219 Signals and Systems 

Mathematics

• MAT290 Advanced Engineering Mathematics

WORK AND VOLUNTEERING

Volunteering

As a volunteer for Engineering Strategies and Practice (ESP) at UofT, I developed multiple engineering design projects for first-year engineering students. Some of the projects included: [A game playing machine that tests human reaction], [An alarm clock that cannot turn off unless the user is awake], [A system for wild animal detection and avoidance], [A smart fridge or recipe recommendation pipeline for the stuck-at-home cook],  [A device or system for making friends at the University of Toronto].

Work

2013 – 2014 Intern, Power System Planning, Ontario Power Authority                                                                              

AWARDS AND FUNDING

2021       Doctoral  Completion Award

2019       University of Toronto Travel Award $1120

2018       Control and Decision (CDC) conference student travel award $400

2015-17  Ontario Graduate Scholarship 

2014       UofT IBBME Laboratory Development Fund – Funding for completion of 3D printed robotic arm and hardware assembly 

2014       UofT Max Weber Undergraduate Award in Sociology – Awards are given to the students achieving the five top grades in St. George sections of SOC101Y Introduction to Sociology 

TECHNICAL SKILLS

I had a relatively late start on many technical skills. My first contact with computer programming was when I started my undergraduate at UofT. I have picked up a tremendous amount of programming languages over the years, such as C, C++, Java, Scheme/Racket, Haskell, VB.Net, VBA, SQL, Bash (Shell), Rust. However, the only language that I use in practice is Python. 

Programming Languages        Python

Machine Learning Libraries   Tensorflow, Pytorch, Keras, JAX/Objax, Sci-kit learn

Software Design Tools              MATLAB (Simulink), Microsoft Excel (VBA), Google Colab, Visual Studio, PyCharm

Hardware Design Tools            Arduino Uno, Xilinx FGPA, Pspice, AutoCad

Operating Systems                   Windows, Unix, MacOS

LANGUAGES

I'm quite enthusiastic about learning different languages. Whenever I travel outside of North America, I would try to learn as much of the local language as possible and converse with the locals. 

Technically conversant        English 

Everyday conversant           Chinese 

Other                                      Spanish (Living in Texas), 

                                                Japanese (Audits)

                                                German (Friends from my ESL class)

                                                Italian (When in Rome...)

                                                French (Living in Canada)

                                                Korean (Self-Study)