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I am reading sutton's reinforcement learning an introduction. The book mentioned that for continuous state space, one could leverage value function with the form

V(s, w) = W*S,

where s represents state and w the weights. So if there is only 1 factor in a state, the function could be like, for instance,

V(s, w) = w_1*s + w_0

However, what if the state has 2 or more components? Say S = S(position, time), then how to rewrite the above function?

Is it V(s, w) = w_1*(position + time) + w_0?

Thanks in advance

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Typically each state represented by a vector in $\mathbb{R}^d$ (likewise for actions).

Then one can write $\hat V(s,\theta) = w^Ts + b$ where $s,w \in \mathbb{R}^2$, $b \in \mathbb{R}$.

Of course this is not really an adequate parameterization of value functions, but just a linear estimator of it.

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