Multi-armed bandits
Choosing the right action in an uncertain world, with provable optimality.
« The multi-armed bandit problem is a classic tale of risk and reward, a timeless struggle between the desire for immediate gratification and the pursuit of long-term gain. It is a tale of temptation and uncertainty, of brave adventurers seeking to maximize their rewards while navigating the treacherous terrain of the unknown. At the heart of this tale lies the enduring question: how do we choose which path to take when confronted with multiple options, each offering its own unique rewards and risks? This is the challenge that confronts us in the multi-armed bandit problem, a formalism that seeks to explore the trade-offs between exploration and exploitation in decision-making. At the core of this problem is the metaphor of the « multi-armed bandit, » a mythical creature with many arms, each holding a slot machine with its own unique payout structure. The adventurer must choose which slot machine to play, knowing that each choice comes with its own reward and risk. Do they play the machines they know will pay out, or do they risk it all on a chance at even greater rewards? This is the dilemma at the heart of the multi-armed bandit problem, a formalism that has captivated the minds of decision-makers and mathematicians alike for generations. It is a problem that continues to challenge and inspire us to this day, as we seek to find the optimal balance between exploration and exploitation in our quest for the greatest rewards. »
Mathematical Statistics
Strengthening theoretical guarantees, and illuminating the understanding of phenomenons and complex systems from pure data.
« Mathematical statistics is a hero among the branches of mathematics, fearlessly tackling the toughest data challenges and emerging victorious with profound insights and reliable predictions. It harnesses the power of theory to strengthen its guarantees and to provide a solid foundation for statistical inference. It serves as a trusted ally to the experimental sciences, helping them to clarify and validate their hypotheses, and to test their theories and models. Last, it illuminates the understanding of complex systems and phenomena, using its statistical techniques and tools to uncover hidden patterns, trends, and relationships in the data. Mathematical statistics is a champion of understanding, using its formidable powers to make the world a better place. »
(Wild) Reinforcement Learning
Acting in a dynamic world that is partially known and adverse, facing obstacles and constraints in an adaptive and optimistic way.
« Reinforcement learning is a valiant and pioneering branch of artificial intelligence, in which agents learn to navigate the dynamic and partially known world with adaptability and optimism. They learn by taking actions and receiving rewards or punishments, and they optimize their behavior over time in order to maximize their reward. This requires them to be adaptive and flexible, to explore and discover new strategies and solutions, and to face obstacles and constraints with courage and determination. Reinforcement learning has the potential to revolutionize the way that we interact with the world, and to enable us to solve complex and challenging problems in innovative and effective ways. It is a field of study that is leading the charge in the quest for artificial intelligence that is intelligent, adaptive, and able to make a positive impact on the world »
Statistical Machine Learning
Building, in an idealistic world, the key statistical tools to understand the what and how of learning.
« Statistical machine learning is a visionary and idealistic field, in which we build powerful statistical tools to unlock the secrets of learning from data. We use these tools to build models that can classify, cluster, forecast, optimize, and discover, and that can shed light on the underlying patterns and structures that govern the world around us. Statistical machine learning is a field that is grounded in the principles of statistical inference, and that is dedicated to building accurate, reliable, robust, and generalizable models that can make a positive impact on the world. It is a field that is leading the charge in the quest for understanding through data, and for using data to make the world a better place. »