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GAE — Generalized Advantage Estimation formula.

hard

Answer

  • AtGAE(γ,  λ)  =  Σl=0A_{t}^{\mathrm{GAE}({\gamma}, \;{\lambda})}\; = \;{\Sigma}_{l = 0}^∞ (γλ)l({\gamma}{\lambda})l δt+l{\delta}_{t + l} where δt  =  rt  +  γ{\delta}_{t}\; = \;r_{t}\; + \;{\gamma} V(st+1)    V(st)V(s_{t + 1})\; - \;V(s_{t}). λ = 0 → TD(0) advantage (biased, low var). λ = 1 → MC advantage (unbiased, high var).
  • Typical λ = 0.95 in PPO.
  • Provides smooth bias-variance tradeoff.
  • Compute efficiently backward from end of trajectory.
  • Standard advantage estimator in modern policy gradient methods.
Check yourself — multiple choice
  • Random
  • AtGAE  =  ΣlA_{t}^{\mathrm{GAE}}\; = \;{\Sigma}_{l} (γλ)l({\gamma}{\lambda})l δt+l{\delta}_{t + l} with δ = r + γV(s') - V(s); λ=0 → TD(0) biased low-var, λ=1 → MC unbiased high-var; PPO uses λ ≈ 0.95
  • Same as TD
  • Not real

GAE(λ): weighted sum of TD errors; PPO default λ ≈ 0.95.

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