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Raihan Seraj

raihan.seraj@mila.quebec
Doctorat - McGill University
Superviseur⋅e principal⋅e
Aditya Mahajan

Publications

Approximate information state for approximate planning and reinforcement learning in partially observed systems
Jayakumar Subramanian
Amit Sinha
Raihan Seraj
Aditya Mahajan
We propose a theoretical framework for approximate planning and learning in partially observed systems. Our framework is based on the fundam… (voir plus)ental notion of information state. We provide two equivalent definitions of information state---i) a function of history which is sufficient to compute the expected reward and predict its next value; ii) equivalently, a function of the history which can be recursively updated and is sufficient to compute the expected reward and predict the next observation. An information state always leads to a dynamic programming decomposition. Our key result is to show that if a function of the history (called approximate information state (AIS)) approximately satisfies the properties of the information state, then there is a corresponding approximate dynamic program. We show that the policy computed using this is approximately optimal with bounded loss of optimality. We show that several approximations in state, observation and action spaces in literature can be viewed as instances of AIS. In some of these cases, we obtain tighter bounds. A salient feature of AIS is that it can be learnt from data. We present AIS based multi-time scale policy gradient algorithms. and detailed numerical experiments with low, moderate and high dimensional environments.
arxiv.org
Mean-field approximation for large-population beauty-contest games
Raihan Seraj
Jerome Le Ny
Aditya Mahajan
We study a class of Keynesian beauty contest games where a large number of heterogeneous players attempt to estimate a common parameter base… (voir plus)d on their own observations. The players are rewarded for producing an estimate close to a certain multiplicative factor of the average decision, this factor being specific to each player. This model is motivated by scenarios arising in commodity or financial markets, where investment decisions are sometimes partly based on following a trend. We provide a method to compute Nash equilibria within the class of affine strategies. We then develop a mean-field approximation, in the limit of an infinite number of players, which has the advantage that computing the best-response strategies only requires the knowledge of the parameter distribution of the players, rather than their actual parameters. We show that the mean-field strategies lead to an ε-Nash equilibrium for a system with a finite number of players. We conclude by analyzing the impact on individual behavior of changes in aggregate population behavior.
2021-12-14
IEEE Conference on Decision and Control (publié)
doi.org