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V-trace off-policy correction formula.

hard

Answer

  • vs  =  V(ss)  +  Σtv_{s}\; = \;V(s_{s})\; + \;{\Sigma}_{t} γts{\gamma}^{t - s} (Π  ρi)({\Pi}\;{\rho}_{i}) δtV{\delta}_{t}^{V} with δtV  =  rt  +  γ{\delta}_{t}^{V}\; = \;r_{t}\; + \;{\gamma} V(st+1)    V(st)V(s_{t + 1})\; - \;V(s_{t}), and ρi  =  min(ρ,  π/μ){\rho}_{i}\; = \;\operatorname{min}({\rho}, \;{\pi} / {\mu}) clipped importance ratio.
  • Different clipping thresholds for ρ (target) vs c (trace) allow bias-variance trade.
  • Off-policy corrections without exploding variance.
  • Enables IMPALA-style distributed training.
  • Modern reference for scalable off-policy actor-critic.
Check yourself — multiple choice
  • Random
  • vs  =  V(ss)  +  Σv_{s}\; = \;V(s_{s})\; + \;{\Sigma} γts{\gamma}^{t - s} (Π  ρi)({\Pi}\;{\rho}_{i}) δtV{\delta}_{t}^{V} with ρi  =  min(ρ,  π/μ){\rho}_{i}\; = \;\operatorname{min}({\rho}, \;{\pi} / {\mu}); separate clipping thresholds for target and trace → tunes bias-variance; enables IMPALA
  • Same as GAE
  • Not real

V-trace: truncated IS + clipping ρ̄ for target and c for trace; IMPALA.

#actor-critic#theory

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