And? This does not address my argument that the complexity is beyond-combinatorially explosive (infinite spaces). I'm not talking about the space of possible board states. I'm talking about merely the set of all possible actions.

EDIT: clarified my language to address below reply.

...and it's possible to train learning agents to sense and interact with a world described by high dimensional continuous vector spaces, for instance using conv nets (for sensing audio / video signals) and actor-critic to learn an continuous policy:

http://arxiv.org/abs/1509.02971

The fact that the (reinforcement) learning problem is hard or not is not directly related to whether the observation and action spaces are discrete or continuous.

see also by the same team:

http://arxiv.org/abs/1602.01783

There is a near infinite number of such spaces.

I don't understand why would the "number of spaces" matters. What matters is can you design a learning algorithm that performs well in interesting spaces such as:

- discrete spaces such as atari games and go, - continuous spaces such as driving a car, controlling a robot or bid on a ad exchange.

A really really large number of distinct decisions that need to be made. A car only needs to control a small set of actions (wheels, engine, a couple others I'm missing). A game player only needs to choose from a small set of actions (e.g. place piece at position X, move left/right/up/down/jump).

A human brain also has a limited number of muscles to control to interact with the world.

And a much larger set of decisions.

Go is combinatorially explosive, too.