PRL Workshop 2020 Workshop Paper
- Sankalp Garg
- Aniket Bajpai
- Mausam Mausam
A Relational Markov Decision Process (RMDP) (Boutilier, Reiter, and Price 2001) is a first-order, predicate calculusbased representation for expressing instances of a probabilistic planning domain with a possibly unbounded number of objects. An RMDP domain has object types, relational state predicate and action symbols that are applied over objects, first order transition templates that specify probabilistic effects associated with action symbols, and a first-order reward structure. A domain instance additionally specifies a set of objects and a start state, thus defining a ground MDP with a known start state (Kolobov, Mausam, and Weld 2012)). Relational planners aim to produce a single generalized policy that can yield a ground policy for all instances of the domain, with little instance-specific computation. Domain-independent planners are representation-specific, but domain-agnostic, making them applicable to all domains expressible in the language. In this paper, we design a domain-independent relational planner. RMDP planners, in their vision, expect to scale to very large problem sizes by exploiting the first-order structures of a domain – thereby reducing the curse of dimensionality. Traditional RMDP planners attempted to find a generalized first-order value function or policy using symbolic dynamic programming (Boutilier, Reiter, and Price 2001), or by approximating them via a function over first-order basis functions (e. g. , (Guestrin et al. 2003; Sanner and Boutilier 2009)). Unfortunately, these methods met with rather limited success, for e. g. , no relational planner participated in International Probabilistic Planning Competition (IPPC)1 after 2006, even though all competition domains were relational. We believe that this lack of success may be due to the inherent limitations in the representation power of a basis function-based representation. Through this work, we wish to revive the research thread on RMDPs and explore if neural models could be effective in representing these first-order functions. We present Symbolic NetWork (S YM N ET), the first domain-independent neural relational planner that computes generalized policies for RMDPs that are expressed in the symbolic representation language of RDDL (Sanner 2010). S YM N ET outputs its generalized policy via a neural model whose all parameters are specific to a domain, but tied among all instances of that domain. So, on a new test instance, the policy can be applied out of the box using pre-trained parameters, i. e. , without any retraining on the test instance. S YM N ET is domain-independent because it converts an RDDL domain file (and instance files) completely automatically into neural architectures, without any human intervention. S YM N ET architecture uses two key ideas. First, it visualizes each state of each domain instance as a graph, where Copyright c 2020, Association for the Advancement of Artificial Intelligence (www. aaai. org). All rights reserved. 1 http: //www. icaps-conference. org/index. php/Main/ Competitions A Relational Markov Decision Process (RMDP) is a firstorder representation to express all instances of a single probabilistic planning domain with possibly unbounded number of objects. Early work in RMDPs outputs generalized (instanceindependent) first-order policies or value functions as a means to solve all instances of a domain at once. Unfortunately, this line of work met with limited success due to inherent limitations of the representation space used in such policies or value functions. Can neural models provide the missing link by easily representing more complex generalized policies, thus making them effective on all instances of a given domain? We present S YM N ET, the first neural approach for solving RMDPs that are expressed in the probabilistic planning language of RDDL. S YM N ET trains a set of shared parameters for an RDDL domain using training instances from that domain. For each instance, S YM N ET first converts it to an instance graph and then uses relational neural models to compute node embeddings. It then scores each ground action as a function over the first-order action symbols and node embeddings related to the action. Given a new test instance from the same domain, S YM N ET architecture with pre-trained parameters scores each ground action and chooses the best action. This can be accomplished in a single forward pass without any retraining on the test instance, thus implicitly representing a neural generalized policy for the whole domain. Our experiments on nine RDDL domains from IPPC demonstrate that S YM N ET policies are significantly better than random and sometimes even more effective than training a state-of-the-art deep reactive policy from scratch.