Epistemic planning is the sub-field of AI planning that focuses on changing knowledge and belief. It is important in both multi-agent domains where agents need to have knowledge/belief regarding the environment, but also the beliefs of other agents, including nested beliefs. When modeling knowledge in multi-agent settings, many models face an exponential growth challenge in terms of nested depth. A contemporary method, known as Planning with Perspectives (PWP), addresses these challenges through the use of perspectives and set operations for knowledge. The JP model defines that an agent's belief is justified if and only if the agent has seen evidence that this belief was true in the past and has not seen evidence to suggest that this has changed. The current paper extends the JP model to handle \emph{group belief}, including distributed belief and common belief. We call this the Group Justified Perspective (GJP) model. Using experimental problems crafted by adapting well-known benchmarks to a group setting, we show the efficiency and expressiveness of our GJP model at handling planning problems that cannot be handled by other epistemic planning tools.

Epistemic Planning (EP) is an important research area dedicated to reasoning about the knowledge and beliefs of agents in multi-agent cooperative or adversarial settings. The Justified Perspective (JP) model is the state-of-the-art approach to solving EP problems with efficiency and expressiveness. However, all existing EP methods inherit the static environment assumption from classical planning. This limitation hinders the application of EP in fields such as robotics with multi-agent settings, where the environment contains changing variables. In this paper, we propose an extension of the JP model, namely, the Predictive Justified Perspective (PJP) model, to remove this assumption. Instead of assuming that beliefs remain unchanged since the last observation, the PJP model uses all past observations to form predictions about the changing variables. The definition of the prediction function with examples is provided, and it is demonstrated that it can work with arbitrary nesting. We then implemented the PJP model in several well-known domains and compared it with the JP model in the experiments. The results indicated that the PJP model performs exceptionally well across various domains, demonstrating its potential in improving EP applications in robotics.

One key decision for heuristic search algorithms is how to balance exploration and exploitation. In classical planning, novelty search has come out as the most successful approach in this respect. The idea is to favor states that contain previously unseen facts when searching for a plan. This is done by maintaining a record of the tuples of facts observed in previous states. Then the novelty of a state is the size of the smallest previously unseen tuple. The most successful version of novelty search is best-first width search (BFWS), which combines novelty measures with heuristic estimates. An orthogonal approach to balance exploration-exploitation is to use several open-lists. These open-lists are ordered using different heuristic estimates, which diversify the information used in the search. The search algorithm then alternates between these open-lists, trying to exploit these different estimates. This is the approach used by LAMA, a classical planner that, a decade after its release, is still considered state-of-the-art in agile planning. In this paper, we study how to combine LAMA and BFWS. We show that simply adding the strongest open-list used in BFWS to LAMA harms performance. However, we show that combining only parts of each planner leads to a new state-of-the-art agile planner.

The Atari 2600 games supported in the Arcade Learning Environment [Bellemare et al., 2013] all feature a known initial (RAM) state and actions that have deterministic effects. Classical planners, however, cannot be used off-the-shelf as there is no compact PDDL-model of the games, and action effects and goals are not known a priori. Indeed, there are no explicit goals, and the planner must select actions on line while interacting with a simulator that returns successor states and rewards. None of this precludes the use of blind lookahead algorithms for action selection like breadth-first search or Dijkstra's yet such methods are not effective over large state spaces. We thus turn to a different class of planning methods introduced recently that have been shown to be effective for solving large planning problems but which do not require prior knowledge of state transitions, costs (rewards) or goals. The empirical results over 54 Atari games show that the simplest such algorithm performs at the level of UCT, the state-of-the-art planning method in this domain, and suggest the potential of width-based methods for planning with simulators when factored, compact action models are not available.

It has been shown recently that heuristic and width-based search can be combined to produce planning algorithms with a performance that goes beyond the state-of-the-art. Such algorithms are based on best-first width search (BFWS), a plain best-first search set with evaluations functions combined lexicographically to break ties, some of which express novelty based preferences.

Width-based algorithms search for solutions through a general definition of state novelty. These algorithms have been shown to result in state-of-the-art performance in classical planning, and have been successfully applied to model-based and model-free settings where the dynamics of the problem are given through simulation engines. Width-based algorithms performance is understood theoretically through the notion of planning width, providing polynomial guarantees on their runtime and memory consumption. To facilitate synergies across research communities, this paper summarizes the area of width-based planning, and surveys current and future research directions.

Width-based search algorithms seek plans by prioritizing states according to a suitably defined measure of novelty, that maps states into a set of novelty categories. Space and time complexity to evaluate state novelty is known to be exponential on the cardinality of the set. We present novel methods to obtain polynomial approximations of novelty and width-based search. First, we approximate novelty computation via random sampling and Bloom filters, reducing the runtime and memory footprint. Second, we approximate the best-first search using an adaptive policy that decides whether to forgo the expansion of nodes in the open list. These two techniques are integrated into existing width-based algorithms, resulting in new planners that perform significantly better than other state-of-the-art planners over benchmarks from the International Planning Competitions.

Width-based search methods have demonstrated state-of-the-art performance in a wide range of testbeds, from classical planning problems to image-based simulators such as Atari games. These methods scale independently of the size of the state-space, but exponentially in the problem width. In practice, running the algorithm with a width larger than 1 is computationally intractable, prohibiting IW from solving higher width problems. In this paper, we present a hierarchical algorithm that plans at two levels of abstraction. A high-level planner uses abstract features that are incrementally discovered from low-level pruning decisions. We illustrate this algorithm in classical planning PDDL domains as well as in pixel-based simulator domains. In classical planning, we show how IW(1) at two levels of abstraction can solve problems of width 2. For pixel-based domains, we show how in combination with a learned policy and a learned value function, the proposed hierarchical IW can outperform current flat IW-based planners in Atari games with sparse rewards.

In multi-agent planning, preserving the agents' privacy has become an increasingly popular research topic. For preserving the agents' privacy, agents jointly compute a plan that achieves mutual goals by keeping certain information private to the individual agents. Unfortunately, this can severely restrict the accuracy of the heuristic functions used while searching for solutions. It has been recently shown that, for centralized planning, the performance of goal oriented search can be improved by combining goal oriented search and width-based search. The combination of these techniques has been called best-first width search. In this paper, we investigate the usage of best-first width search in the context of (decentralised) multi-agent privacy-preserving planning, addressing the challenges related to the agents' privacy and performance. In particular, we show that best-first width search is a very effective approach over several benchmark domains, even when the search is driven by heuristics that roughly estimate the distance from goal states, computed without using the private information of other agents. An experimental study analyses the effectiveness of our techniques and compares them with the state-of-the-art.

Width-based planning has demonstrated great success in recent years due to its ability to scale independently of the size of the state space. For example, Bandres et al. (2018) introduced a rollout version of the Iterated Width algorithm whose performance compares well with humans and learning methods in the pixel setting of the Atari games suite. In this setting, planning is done on-line using the "screen" states and selecting actions by looking ahead into the future. However, this algorithm is purely exploratory and does not leverage past reward information. Furthermore, it requires the state to be factored into features that need to be pre-defined for the particular task, e.g., the B-PROST pixel features. In this work, we extend width-based planning by incorporating an explicit policy in the action selection mechanism. Our method, called $\pi$-IW, interleaves width-based planning and policy learning using the state-actions visited by the planner. The policy estimate takes the form of a neural network and is in turn used to guide the planning step, thus reinforcing promising paths. Surprisingly, we observe that the representation learned by the neural network can be used as a feature space for the width-based planner without degrading its performance, thus removing the requirement of pre-defined features for the planner. We compare $\pi$-IW with previous width-based methods and with AlphaZero, a method that also interleaves planning and learning, in simple environments, and show that $\pi$-IW has superior performance. We also show that $\pi$-IW algorithm outperforms previous width-based methods in the pixel setting of Atari games suite.