Linear Function Approximation in Reinforcement Learning

Author(s): Shivam Mohan

Originally published on Towards AI.

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In reinforcement learning (RL), a key challenge is estimating the value function, which predicts future rewards based on the current state. In large or continuous state spaces, it’s often impractical to explicitly store or compute the value function for every possible state. This is where function approximation becomes essential, allowing us to generalize the value of unseen states from observed ones.

A widely used approach in Reinforcement Learning is Linear Function Approximation. Here, instead of learning the value of each state individually, we represent the value function as a weighted combination of features of that state. Mathematically, we express the estimated value function V(s) as:

V(s) ≈ w_1 * φ_1(s) + w_2 * φ_2(s) + … + w_k * φ_k(s)

Where:

w is a vector of weights (parameters) that we aim to learn.φ(s) is a vector of features (or basis functions) that describe the state.

Each feature φ_i(s) represents a specific characteristic of the state. For example, in a Pac-Man-like environment:

φ_1(s) could represent the distance to the nearest dot.φ_2(s) might represent the inverse distance to the nearest ghost.

By learning the appropriate weights for these features, we can approximate the value function V(s) across the… Read the full blog for free on Medium.

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Published via Towards AI