Partial Observability, Randomness, and God
Tuesday, May 17th, 2011My research is in the area of reinforcement learning, where an agent is learning to solve a sequential decision making task. In it, the agent takes an action from state, which leads it to some new state and provides it some reward. The outcome of the actions can be noisy or random. For example, when you’re driving your car and you make a decision to take a particular turn, there is some noise in the outcome (you can not predict deterministically what will happen). Instead, there may be construction, traffic, pedestrians, etc which cause your trip down this road to take longer or shorter than you would expect. You can’t predict exactly the number of seconds it will take. However, this randomness, at its core, is really the result of partial observability. Partial observability is where you can only observe some part of the world to make your prediction. In this example, you only have access to what you see at the intersection and the info you get from the internet, radio, tv, and your phone. With this information, you cannot predict the time the road will take precisely and instead there is some noise to it. However, if you knew what every other driver was thinking and the route and timings they would take, along with what the weather would do, what the exact construction plans were, etc, then you could conceivably make this prediction accurately (or a computer could). So you can view this decision making task as having noise or being partially observable. This goes on at all levels, but at some point you would need knowledge of every atom and molecule in the system (which can’t be observed), so its easier to approximate things as being noisy. But as we get better and better at observing such things, we can make more deterministic predictions that consider all the factors that we previously ignored as “noise.”
A lot of interviews I’ve seen with sports stars recently has made me think of this. I’ve seen quite a few instances (like this one: http://msn.foxsports.com/nfl/story/buffalo-bills-stevie-johnson-blames-god) of some seemingly random event happening, and the athlete’s response is to credit it to God. Instead of believing in randomness, they believe the world is partially observable and God is the hidden observation that can not be seen. Random events aren’t random, but instead are things that God did, and of course we couldn’t observe God’s decision making process. Anyway, I thought this connection was interesting, I’m not sure if its better to think there’s some force deciding all outcomes or to think that some things do just happen randomly. But it’s an interesting question: Is God simply an non-observed feature of the world state?