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+with+continuous+state+and+action+spaces+remains+one+of+the+most+challenging+problems+within+the+field.+Most+current+learning+methods+focus+on+integral+identities+such+as+value+functions+to+derive+an+optimal+strategy+for+the+learning+agent.+In+this+paper%252C+we+instead+study+the+dual+form+of+the+original+RL+formulation+to+propose+the+first+differential+RL+framework+that+can+handle+settings+with+limited+training+samples+and+short-length+episodes.+Our+approach+introduces+Differential+Policy+Optimization+(DPO)%252C+a+pointwise+and+stage-wise+iteration+method+that+optimizes+policies+encoded+by+local-movement+operators.+We+prove+a+pointwise+convergence+estimate+for+DPO+and+provide+a+regret+bound+comparable+with+the+best+current+theoretical+derivation.+Such+pointwise+estimate+ensures+that+the+learned+policy+matches+the+optimal+path+uniformly+across+different+steps.+We+then+apply+DPO+to+a+class+of+practical+RL+problems+with+continuous+state+and+action+spaces%252C+and+which+search+for+optimal+configurations+with+Lagrangian+rewards.+DPO+is+easy+to+implement%252C+scalable%252C+and+shows+competitive+results+on+benchmarking+experiments+against+several+popular+RL+methods.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.089e0c8dcd23ffb7abe51408a07d3ed3%3frik%3dwUsjWvcg4Cnzxg%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=DPO+Reinforcement+Learning&FORM=IRPRST&ck=08762270A3D312E08DF787AFCA7EE0D9&selectedIndex=0&itb=0)
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