LaValle Planning Algorithms, ch 9


[Where I stopped reading so carefully, covers game theory]

  • (360) Treats stochasticity  as a multi-player game
  • (361) As in motion planning, an optimal decision may not exist because of open sets
  • (369) Minimax solution has best worst case bounds
  • Stochasticity is separated into nondeterminism and probabalistic stochasticity, adversarial vs nonadversarial
  • (373) Optimal decision making in terms of classification
    • (377) Param estimation
  • (381) When using randomized strategies, the values for both players’ optimal actions can be equal in any 0-sum game, isn’t generally true of randomized policies.
  • (382) Not all zero sum games have an equilibrium when deterministic strategies are used
  • (384) Finding an equilibria for randomized policies can be done utilizing the following:
    • Security strategy for ea player can be found by only looking at deterministic strategies for other player
    • If strategy for other player is fixed expected cost is a linear f() of action prbs
  • (390) Computing Nash equilibria is harder than the above because of finding saddle points (?)
  • (399) “The frequentist approach attempts to be more conservative and rigorous, with the result being that weaker statements are made regarding decisions.”
  • (400) MaxEnt
  • (402) Argument against worst-case analysis
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