Knowledge-based programs as succinct policies for partially observable domains

Abstract We suggest to express policies for contingent planning by knowledge-based programs (KBPs). KBPs, introduced by Fagin et al. (1995) [32] , are high-level protocols describing the actions that the agent should perform as a function of their current knowledge: branching conditions are epistemic formulas that are interpretable by the agent. The main aim of our paper is to show that KBPs can be seen as a succinct language for expressing policies in single-agent contingent planning. KBP are conceptually very close to languages used for expressing policies in the partially observable planning literature: like them, they have conditional and looping structures, with actions as atomic programs and Boolean formulas on beliefs for choosing the execution path. Now, the specificity of KBPs is that branching conditions refer to the belief state and not to the observations. Because of their structural proximity, KBPs and standard languages for representing policies have the same power of expressivity: every standard policy can be expressed as a KBP, and every KBP can be “unfolded” into a standard policy. However, KBPs are more succinct, more readable, and more explainable than standard policies. On the other hand, they require more online computation time, but we show that this is an unavoidable tradeoff. We study knowledge-based programs along four criteria: expressivity, succinctness, complexity of online execution, and complexity of verification.

[1]  Marco Pistore,et al.  Weak, strong, and strong cyclic planning via symbolic model checking , 2003, Artif. Intell..

[2]  Pierre Marquis,et al.  A Knowledge Compilation Map , 2002, J. Artif. Intell. Res..

[3]  Craig Boutilier,et al.  Bounded Finite State Controllers , 2003, NIPS.

[4]  Lane A. Hemachandra,et al.  The strong exponential hierarchy collapses , 1989 .

[5]  Samuel R. Buss,et al.  On Truth-Table Reducibility to SAT , 1991, Inf. Comput..

[6]  Giuseppe De Giacomo,et al.  Bounded situation calculus action theories , 2015, Artif. Intell..

[7]  Thomas Bolander,et al.  Conditional Epistemic Planning , 2012, JELIA.

[8]  Blai Bonet,et al.  Planning with Incomplete Information as Heuristic Search in Belief Space , 2000, AIPS.

[9]  Leora Morgenstern,et al.  Knowledge Preconditions for Actions and Plans , 1988, IJCAI.

[10]  Hector Geffner,et al.  Compiling Uncertainty Away in Non-Deterministic Conformant Planning , 2010, ECAI.

[11]  Richard J. Lipton,et al.  Some connections between nonuniform and uniform complexity classes , 1980, STOC '80.

[12]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[13]  Tran Cao Son,et al.  Formalizing sensing actions A transition function based approach , 2001, Artif. Intell..

[14]  Andreas Witzel,et al.  DEL Planning and Some Tractable Cases , 2011, LORI.

[15]  Paolo Traverso,et al.  Automated Planning and Acting , 2016 .

[16]  Jens Claßen,et al.  Decidable Verification of Golog Programs over Non-Local Effect Actions , 2016, AAAI.

[17]  Karl Johan Åström,et al.  Optimal control of Markov processes with incomplete state information , 1965 .

[18]  Raymond Reiter,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2001 .

[19]  R. Brafman,et al.  Contingent Planning via Heuristic Forward Search witn Implicit Belief States , 2005, ICAPS.

[20]  Hector Geffner,et al.  Planning under Partial Observability by Classical Replanning: Theory and Experiments , 2011, IJCAI.

[21]  François Schwarzentruber,et al.  Hintikka's World: Scalable Higher-order Knowledge , 2019, IJCAI.

[22]  Yanjing Wang,et al.  More for free: a dynamic epistemic framework for conformant planning over transition systems , 2017, J. Log. Comput..

[23]  Guillaume Aucher,et al.  DEL-sequents for regression and epistemic planning , 2012, J. Appl. Non Class. Logics.

[24]  Blai Bonet,et al.  A Concise Introduction to Models and Methods for Automated Planning , 2013, A Concise Introduction to Models and Methods for Automated Planning.

[25]  Jérôme Lang,et al.  Knowledge-Based Programs as Plans - The Complexity of Plan Verification , 2012, ECAI.

[26]  Christian J. Muise,et al.  Computing Contingent Plans via Fully Observable Non-Deterministic Planning , 2014, AAAI.

[27]  Patrik Haslum,et al.  Some Results on the Complexity of Planning with Incomplete Information , 1999, ECP.

[28]  Iris van Rooij,et al.  Minesweeper May Not Be NP-Complete but Is Hard Nonetheless , 2011 .

[29]  Jérôme Lang,et al.  Knowledge-Based Programs as Plans: Succinctness and the Complexity of Plan Existence , 2013, TARK.

[30]  Piergiorgio Bertoli,et al.  Strong planning under partial observability , 2006, Artif. Intell..

[31]  Blai Bonet,et al.  Flexible and Scalable Partially Observable Planning with Linear Translations , 2014, AAAI.

[32]  Gerhard Lakemeyer,et al.  Foundations for Knowledge-Based Programs using ES , 2006, KR.

[33]  François Schwarzentruber,et al.  Knowledge-Based Policies for Qualitative Decentralized POMDPs , 2018, AAAI.

[34]  Hector Geffner,et al.  A Translation-Based Approach to Contingent Planning , 2009, IJCAI.

[35]  Enrico Pontelli,et al.  A generic approach to planning in the presence of incomplete information: Theory and implementation , 2015, Artif. Intell..

[36]  Fahiem Bacchus,et al.  Extending the Knowledge-Based Approach to Planning with Incomplete Information and Sensing , 2004, ICAPS.

[37]  Christer Bäckström,et al.  Algorithms and Limits for Compact Plan Representations , 2012, J. Artif. Intell. Res..

[38]  Moshe Y. Vardi,et al.  L O ] 2 4 Ju l 2 01 3 Synthesis from Knowledge-Based Specifications ⋆ , 2014 .

[39]  Guy Shani,et al.  Qualitative Planning under Partial Observability in Multi-Agent Domains , 2013, AAAI.

[40]  Giuseppe De Giacomo,et al.  Progression and Verification of Situation Calculus Agents with Bounded Beliefs , 2014, Studia Logica.

[41]  Jérôme Lang,et al.  From Knowledge-based Programs to Graded Belief-based Programs, Part I: On-line Reasoning* , 2004, Synthese.

[42]  Thomas Bolander,et al.  Epistemic planning for single- and multi-agent systems , 2011, J. Appl. Non Class. Logics.

[43]  Joelle Pineau,et al.  Anytime Point-Based Approximations for Large POMDPs , 2006, J. Artif. Intell. Res..

[44]  Neil Immerman,et al.  The Complexity of Decentralized Control of Markov Decision Processes , 2000, UAI.

[45]  Hector J. Levesque,et al.  ALLEGRO: Belief-Based Programming in Stochastic Dynamical Domains , 2015, IJCAI.

[46]  François Schwarzentruber,et al.  Hintikka's World: Agents with Higher-order Knowledge , 2018, IJCAI.

[47]  Guy Shani,et al.  Online belief tracking using regression for contingent planning , 2016, Artif. Intell..

[48]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[49]  Mikhail Soutchanski,et al.  Decidable Reasoning in a Modified Situation Calculus , 2007, IJCAI.

[50]  Jussi Rintanen,et al.  Complexity of Planning with Partial Observability , 2004, ICAPS.

[51]  Robert C. Moore.  A Formal Theory of Knowledge and Action , 1984 .

[52]  Ronen I. Brafman,et al.  On the Knowledge Requirements of Tasks , 1998, Artif. Intell..

[53]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[54]  Bernhard Nebel,et al.  The Dynamic Logic of Policies and Contingent Planning , 2019, JELIA.

[55]  Christer Bäckström,et al.  Automaton Plans , 2014, J. Artif. Intell. Res..

[56]  Blai Bonet,et al.  Belief Tracking for Planning with Sensing: Width, Complexity and Approximations , 2014, J. Artif. Intell. Res..

[57]  Klaus W. Wagner,et al.  Bounded Query Classes , 1990, SIAM J. Comput..

[58]  Jens Claßen,et al.  Verification of Knowledge-Based Programs over Description Logic Actions , 2015, IJCAI.

[59]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[60]  Thomas Bolander,et al.  Undecidability in Epistemic Planning , 2013, IJCAI.

[61]  Daniel Bryce,et al.  State agnostic planning graphs: deterministic, non-deterministic, and probabilistic planning , 2011, Artif. Intell..

[62]  Guy Shani,et al.  Replanning in Domains with Partial Information and Sensing Actions , 2012, J. Artif. Intell. Res..

[63]  Enrico Giunchiglia,et al.  Planning as Satisfiability in Nondeterministic Domains , 2000, AAAI/IAAI.

[64]  Jussi Rintanen,et al.  Conditional Planning in the Discrete Belief Space , 2005, IJCAI.

[65]  Bernhard Nebel,et al.  On the Compilability and Expressive Power of Propositional Planning Formalisms , 2000, J. Artif. Intell. Res..

[66]  Lars Karlsson,et al.  Conditional progressive planning under uncertainty , 2001, IJCAI.

[67]  Jorge A. Baier,et al.  On Planning with Programs that Sense , 2006, KR.

[68]  Andreas Herzig,et al.  Action representation and partially observable planning using epistemic logic , 2003, IJCAI.

[69]  Edward J. Sondik,et al.  The Optimal Control of Partially Observable Markov Processes over a Finite Horizon , 1973, Oper. Res..

[70]  Jens Claßen,et al.  Knowledge-Based Programs with Defaults in a Modal Situation Calculus , 2016, ECAI.

[71]  Albert R. Meyer,et al.  The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.

[72]  Shlomi Maliah,et al.  Partially Observable Online Contingent Planning Using Landmark Heuristics , 2014, ICAPS.

[73]  Jérôme Lang,et al.  From knowledge-based programs to graded belief-based programs, part II: off-line reasoning , 2005, IJCAI 2005.