Eligibility trace update: e(t+1) = λ·e(t) + x_pre·x_post · @brief Eligibility trace update: e(t+1)

Read the equation

This relation defines @brief Eligibility trace update: e(t+1) in the source section “Eligibility trace update: e(t+1) = λ·e(t) + x_pre·x_post · @brief Eligibility trace update: e(t+1)”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read @brief Eligibility trace update: e(t+1) as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

 */
inline double three_factor_learning(double x_pre, double x_post, double reward,
                                      double eligibility = 1.0, double eta = ETA) {
    return eta * x_pre * x_post * reward * eligibility;
}

/**
 * @brief Eligibility trace update: e(t+1) = λ·e(t) + x_pre·x_post
 */
inline double eligibility_update(double trace, double x_pre, double x_post, double lambda = 0.9) {
    return lambda * trace + x_pre * x_post;
}

/**
 * @brief TD error: δ = r + γV(s') - V(s)
 */
inline double td_error(double reward, double value_next, double value_current, double gamma_discount = 0.99) {
    return reward + gamma_discount * value_next - value_current;

@brief Eligibility trace update: e(t+1) = λ·e(t) + x_pre·x_post

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