Upper bounds of alpha vectors QMDP and FIB represents an upper bound of the true optimal alpha vector values. QMDP Fast Informed Bound FIB is a generally lower bound than QMDP. Lower bounds of alpha vectors BAWS and blind lower bound represents Faster: best-action worst-state blind lower bound Slower: Point-Based Value Iteration “Perseus”: Randomized PBVI HSVI SARSOP point selection see point selection