I'm interested in (Deep) Reinforcement Learning (RL). Before diving into this field should I take a course in Game Theory (GT)?
How are GT and RL related?
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In Reinforcement Learning (RL) it is common to imagine an underlying Markov Decision Process (MDP). Then the goal of RL is to learn a good policy for the MDP, which is often only partially specified. MDPs can have different objectives such as total, average, or discounted reward, where discounted reward is the most common assumption for RL. There are well-studied extensions of MDPs to two-player (i.e., game) settings; see, e.g.,
Filar, Jerzy, and Koos Vrieze. Competitive Markov decision processes. Springer Science & Business Media, 2012.
There is an underlying theory shared by MDPs and their extensions to two-player (zero-sum) games, including, e.g., the Banach fixed point theorem, Value Iteration, Bellman Optimality, Policy Iteration/Strategy Improvement etc. However, while there are these close connections between MDPs (and thus RL) and these specific type of games:
Game theory is quite involved in the context of Multi-agent Reinforcement learning (MARL).
Take a look at stochastic games or read the article An Analysis of Stochastic Game Theory for Multiagent Reinforcement Learning.
I would not see GT as a prerequisite for RL. However, it provides a nice extension to the multi-agent case.
RL: A single agent is trained to solve a Markov decision problem (MDPS). GT: Two agents are trained to solve Games. A multi-agent Reinforcement learning (MARL) can be used to solve for stochastic games.
If you are interested in the single-agent application of RL in deep learning, then you do not need to go for any GT course. For two or more agents you may need to know the game-theoretic techniques.