By Csaba Szepesvari

Reinforcement studying is a studying paradigm serious about studying to manage a method in order to maximise a numerical functionality degree that expresses a long term objective.What distinguishes reinforcement studying from supervised studying is that merely partial suggestions is given to the learner in regards to the learner's predictions. extra, the predictions can have long-term results via influencing the longer term country of the managed procedure. therefore, time performs a distinct position. The aim in reinforcement studying is to improve effective studying algorithms, in addition to to appreciate the algorithms' benefits and obstacles. Reinforcement studying is of significant curiosity end result of the huge variety of useful functions that it may be used to handle, starting from difficulties in man made intelligence to operations learn or regulate engineering. during this ebook, we concentrate on these algorithms of reinforcement studying that construct at the robust concept of dynamic programming.We supply a reasonably accomplished catalog of studying difficulties, describe the center principles, observe quite a few state-of-the-art algorithms, by means of the dialogue in their theoretical homes and boundaries.

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**Additional resources for Algorithms for Reinforcement Learning **

**Example text**

2. ALGORITHMS FOR LARGE STATE SPACES 31 Algorithm 7 The function implementing the batch-mode λ-LSPE update. This function must be called repeatedly until convergence. function LambdaLSPE(D, θ ) Input: D = ((Xt , At , Rt+1 , Yt+1 ); t = 0, . . , n − 1) is a list of transitions, θ ∈ Rd is the parameter vector 1: A, b, δ ← 0 A ∈ Rd×d , b ∈ Rd , δ ∈ R 2: for t = n − 1 downto 0 do 3: f ← ϕ[Xt ] 4: v←θ f 5: δ ← γ · λ · δ + Rt+1 + γ · θ ϕ[Yt+1 ] − v 6: b ← b + (v + δ) · f 7: A←A+f ·f 8: end for 9: θ ← A−1 b 10: θ ← θ + α · (θ − θ) 11: return θ Thus, in this case, λ-LSPE solves a linear regression problem, implementing the so-called fitted value iteration algorithm for policy evaluation with linear function approximation.

Ik ) (x) = ϕi1 (x1 )ϕi2 (x2 ) . . ϕik (xk ). When X ⊂ Rk , one particularly popular choice is to (1) (d ) use radial basis function (RBF) networks, when ϕ (i) (xi ) = (G(|xi − xi |), . . , G(|xi − xi i |)) . (j ) Here xi ∈ R (j = 1, . . , di ) is fixed by the user and G is a suitable function. A typical choice for G is G(z) = exp(−η z2 ) where η > 0 is a scale parameter. The tensor product construct in this cases places Gaussians at points of a regular grid and the i th basis function becomes ϕi (x) = exp(−η x − x (i) 2 ), where x (i) ∈ X now denotes a point on a regular d1 × .

VALUE PREDICTION PROBLEMS The curse of dimensionality The issue with tensor product constructions, state aggregation and straightforward tile coding is that when the state space is high dimensional they quickly become intractable: For example, a tiling of [0, 1]D with cubical regions with side-lengths of ε gives rise to d = ε −D -dimensional feature- and parameter-vectors. If ε = 1/2 and D = 100, we get the enormous number d ≈ 1030 . This is problematic since state-representations with hundreds of dimensions are common in applications.