Approximate Dynamic Programming with Parallel Stochastic Planning Operators

This thesis presents an approximate dynamic programming (ADP) technique for environment modelling agents. The agent learns a set of parallel stochastic planning operators (P-SPOs) by evaluating changes in its environment in response to actions, using an association rule mining approach. An approximate policy is then derived by iteratively improving state value aggregation estimates attached to the operators using the P-SPOs as a model in a Dyna-Q-like architecture. Reinforcement learning and dynamic programming are powerful techniques for automated agent decision making in stochastic environments. Dynamic programming is effective when there is a known environment model, while reinforcement learning is effective when a model is not available. The techniques derive a policy: a mapping from each environment state to an action which optimizes the long term reward the agent receives. The standard methods become less effective as the state space for the environment increases because they require values to be associated with each state, the storage and processing of which is exponential to the number of state variables. Resolving this “curse of dimensionality” is an important topic of research amongst all communities working on this problem. Two key methods are to: (i) derive an estimate of the value (approximate dynamic programming) using function approximation or state aggregation; or (ii) build a model of the environment from experience. This thesis presents a method of combining these approaches by exploiting structure in the state transition and value functions captured in a set of planning operators which are learnt through experience in the environment. Standard planning operators define the deterministic changes that occur in an environment in response to an action. This work presents Parallel Stochastic Planning Operators (P-SPOs), a novel form of planning operator providing a structured model of the state transition function in environments which are both non-deterministic and for which changes can occur outside the influence of actions. Next, an automated method for extracting P-SPOs from observations in an environment is explored using an adaptation of association rule mining. Finally, methods of relating the state transition structure encapsulated in the P-SPOs to state values, using the operators to store state value aggregation estimates, are evaluated. The framework described provides a method by which approximate dynamic programming can be applied by designers of AI agents and AI planning systems for which they have minimal prior knowledge. The framework and P-SPO based implementations are tested against standard techniques in two bench-mark stochastic environments: a “slippery gripper” block painting robot; and a “predator-prey” agent environment. Experimental results show that an agent using a P-SPO-based approach is able to learn an accurate model of its environment if successor state variables exhibit conditional independence, and an approximate model in the non-independent case. Results also demonstrate that the agent’s ability to generalise to previously unseen states using the model allow it to form an improved policy over an agent employing a standard Dyna-Q based technique. Finally, an approximate policy stored in state aggregation estimates attached to operators is shown to be optimal in experiments for which the P-SPO set contains sufficient information for effective aggregations to be formed

Approximate Dynamic Programming with Parallel Stochastic Planning Operators

This report presents an approximate dynamic programming (ADP) technique for environment modelling agents. The agent learns a set of parallel stochastic planning operators (P-SPOs) by evaluating changes in its environment in response to actions, using an association rule mining approach. An approximate policy is then derived by iteratively improving state value aggregation estimates attached to the operators using the P-SPOs as a model in a Dyna-Q-like architecture. Reinforcement learning and dynamic programming are powerful techniques for automated agent decision making in stochastic environments. Dynamic programming is effective when there is a known environment model, while reinforcement learning is effective when a model is not available. The techniques derive a policy: a mapping from each environment state to an action which optimizes the long term reward the agent receives. The standard methods become less effective as the state space for the environment increases because they require values to be associated with each state, the storage and processing of which is exponential to the number of state variables. Resolving this “curse of dimensionality” is an important topic of research amongst all communities working on this problem. Two key methods are to: (i) derive an estimate of the value (approximate dynamic programming) using function approximation or state aggregation; or (ii) build a model of the environment from experience. This report presents a method of combining these approaches by exploiting structure in the state transition and value functions captured in a set of planning operators which are learnt through experience in the environment. Standard planning operators define the deterministic changes that occur in an environment in response to an action. This work presents Parallel Stochastic Planning Operators (P-SPOs), a novel form of planning operator providing a structured model of the state transition function in environments which are both non-deterministic and for which changes can occur outside the influence of actions. Next, an automated method for extracting P-SPOs from observations in an environment is explored using an adaptation of association rule mining. Finally, methods of relating the state transition structure encapsulated in the P-SPOs to state values, using the operators to store state value aggregation estimates, are evaluated. The framework described provides a method by which approximate dynamic programming can be applied by designers of AI agents and AI planning systems for which they have minimal prior knowledge. The framework and P-SPO based implementations are tested against standard techniques in two bench-mark stochastic environments: a “slippery gripper” block painting robot; and a “predator-prey” agent environment. Experimental results show that an agent using a P-SPO-based approach is able to learn an accurate model of its environment if successor state variables exhibit conditional independence, and an approximate model in the non-independent case. Results also demonstrate that the agent’s ability to generalise to previously unseen states using the model allow it to form an improved policy over an agent employing a standard Dyna-Q based technique. Finally, an approximate policy stored in state aggregation estimates attached to operators is shown to be optimal in experiments for which the P-SPO set contains sufficient information for effective aggregations to be formed

Increasing the Action Gap: New Operators for Reinforcement Learning

This paper introduces new optimality-preserving operators on Q-functions. We first describe an operator for tabular representations, the consistent Bellman operator, which incorporates a notion of local policy consistency. We show that this local consistency leads to an increase in the action gap at each state; increasing this gap, we argue, mitigates the undesirable effects of approximation and estimation errors on the induced greedy policies. This operator can also be applied to discretized continuous space and time problems, and we provide empirical results evidencing superior performance in this context. Extending the idea of a locally consistent operator, we then derive sufficient conditions for an operator to preserve optimality, leading to a family of operators which includes our consistent Bellman operator. As corollaries we provide a proof of optimality for Baird's advantage learning algorithm and derive other gap-increasing operators with interesting properties. We conclude with an empirical study on 60 Atari 2600 games illustrating the strong potential of these new operators

Strategies for dynamic appointment making by container terminals

We consider a container terminal that has to make appointments with barges dynamically, in real-time, and partly automatic. The challenge for the terminal is to make appointments with only limited knowledge about future arriving barges, and in the view of uncertainty and disturbances, such as uncertain arrival and handling times, as well as cancellations and no-shows. We illustrate this problem using an innovative implementation project which is currently running in the Port of Rotterdam. This project aims to align barge rotations and terminal quay schedules by means of a multi-agent system. In this\ud paper, we take the perspective of a single terminal that will participate in this planning system, and focus on the decision making capabilities of its intelligent agent. We focus on the question how the terminal operator can optimize, on an operational level, the utilization of its quay resources, while making reliable appointments with barges, i.e., with a guaranteed departure time. We explore two approaches: (i) an analytical approach based on the value of having certain intervals within the schedule and (ii) an approach based on sources of exibility that are naturally available to the terminal. We use simulation to get insight in the benefits of these approaches. We conclude that a major increase in utilization degree could be achieved only by deploying the sources of exibility, without harming the waiting time of barges too much