Bilateral　filters　have　been　used　for　achieving　excellent　edge-preserving　image　smoothing.　However,　most　studies　have　focused　on　the　acceleration　of　bilateral　filtering　but　not　on　the　stability　of　filtering　process　in　regard　to　small　perturbations　to　its　inputs.　In　this　paper,　we　propose　a　novel　actor-critic　bilateral　filter　trained　with　a　multistep　learning　scheme　for　high-stability　edge-preserving　image　smoothing.　We　first　designed　an　edge-preserving　smoothing　process　as　a　Markov　decision　process　that　involves　adjusting　the　width　setting　for　the　range　kernel　of　a　bilateral　filter.　Next,　we　trained　our　actor-critic　bilateral　filter　in　a　multistep　manner　to　learn　the　optimal　sequence　of　width　settings.　Through　extensive　experiments　on　five　benchmark　datasets,　we　determined　that　the　proposed　actor-critic　bilateral　filter　produced　satisfactory　edge-preserving　smoothing　results.　©　2022　IEEE.