Counterexample Construction
The paper constructs a finite-state counterexample where local-clock differential TD remains stable but global-clock differential TD is unstable. The smallest explicit instance has 25 states. In the counterexample, A_eta is stable exactly…
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The paper constructs a finite-state counterexample where local-clock differential TD remains stable but global-clock differential TD is unstable. The smallest explicit instance has 25 states. In the counterexample, A_eta is stable exactly for eta in two disjoint intervals. The counterexample establishes existence and mechanism rather than frequency in typical benchmarks. The explicit counterexample uses m + 2 states with m greater than 22. The constructed P_pi is row-stochastic, irreducible, and aperiodic.