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The paper introduces DiSProD, an online planner developed for environments with probabilistic transitions in continuous state and action spaces. DiSProD builds a symbolic graph that captures the distribution of future trajectories, conditioned on a given policy, using independence assumptions and approximate propagation of distributions. The symbolic graph provides a differentiable representation of the policy's value, enabling efficient gradient-based optimization for long-horizon search. The propagation of approximate distributions can be seen as an aggregation of many trajectories, making it well-suited for dealing with sparse rewards and stochastic environments. An extensive experimental evaluation compares DiSProD to state-of-the-art planners in discrete-time planning and real-time control of robotic systems. The proposed method improves over existing planners in handling stochastic environments, sensitivity to search depth, sparsity of rewards, and large action spaces. Additional real-world experiments demonstrate that DiSProD can control ground vehicles and surface vessels to successfully navigate around obstacles.

We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a set of fixed vertices and the available connections between them change over time in a predefined manner. We observe that, in some cases, shifting some connections, i.e., advancing or delaying them, can decrease the time required to reach from some vertex (source) to another vertex. We study how we can minimize the maximum time a set of sources needs to reach every vertex, when we are allowed to shift some of the connections. If we restrict the allowed number of changes, we prove that, already for a single source, the problem is NP-hard, and W[2]-hard when parameterized by the number of changes. Then we focus on unconstrained number of changes. We derive a polynomial-time algorithm when there is one source. When there are two sources, we show that the problem becomes NP-hard; on the other hand, we design an FPT algorithm parameterized by the treewidth of the graph plus the lifetime of the optimal solution, that works for any number of sources. Finally, we provide polynomial-time algorithms for several graph classes.

Bounded numeric planning, where each numeric variable domain is bounded, is PSPACE-complete, but such a complexity result does not capture how hard it really is, since the same holds even for the practically much easier STRIPS fragment. A finer way to compare the difficulty of planning formalisms is through the notion of compilability, which has been however extensively studied only for classical planning by Nebel. This paper extends Nebel's framework to the setting of bounded numeric planning. First, we identify a variety of numeric fragments differing on the degree of the polynomials involved and the availability of features such as conditional effects and Boolean conditions; then we study the compilability of these fragments to each other and to the classical fragments. Surprisingly, numeric and classical planning with conditional effects and Boolean conditions can be compiled both ways preserving plan size exactly, while the same does not hold when targeting pure STRIPS. Our study reveals also that numeric fragments cluster into two equivalence classes separated by the availability of incomplete initial state specifications, a feature allowing to specify uncertainty in the initial state.

This paper studies the use of Curriculum Learning on Reinforcement Learning (RL) to improve the performance of the dispatching policies learned on the Job-shop Scheduling Problem (JSP). Current works in the literature present a large optimality gap when learning end-to-end solutions on this problem. In this regard, we identify the difficulty for RL to learn directly on large instances as part of the issue and use Curriculum Learning (CL) to mitigate this effect. Particularly, CL sequences the learning process in a curriculum of increasing complexity tasks, which allows learning on large instances that otherwise would be impossible to learn from scratch. In this paper, we present a size-agnostic model that enables us to demonstrate that current curriculum strategies have a major impact on the quality of the solution inferred. In addition, we introduce a novel Reinforced Adaptive Staircase Curriculum Learning (RASCL) strategy, which adjusts the difficulty level during the learning process by revisiting the worst-performing instances. Conducted experiments on Taillard’s and Demirkol’s datasets show that the presented approach significantly improves the current stateof-the-art models on the JSP. It reduces the average optimality gap from 19.35% to 10.46% on Taillard’s instances and from 38.43% to 18.85% on Demirkol’s instances.

Evacuation planning is a crucial part of disaster management. However, joint optimization of its two essential components, routing and scheduling, with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that utilizes heuristic search with mathematical optimization and can optimize a variety of objective functions. We also present the method MIP-LNS-SIM, where we combine agent-based simulation with MIP-LNS to estimate delays due to congestion, as well as, find optimized plans considering such delays. We use Harris County in Houston, Texas, as our study area. We show that, within a given time limit, MIP-LNS finds better solutions than existing methods in terms of three different metrics. However, when congestion dependent delay is considered, MIP-LNS-SIM outperforms MIP-LNS in multiple performance metrics. In addition, MIP-LNS-SIM has a significantly lower percent error in estimated evacuation completion time compared to MIP-LNS.

Top-k planning, the task of finding k top-cost plans, is a key formalism for many planning applications and K* search is a well-established approach to top-k planning. The algorithm iteratively runs A* search and Eppstein’s algorithm until a sufficient number of plans is found. The performance of K* algorithm is therefore inherently limited by the performance of A*, and in order to improve K* performance, that of A* must be improved. In cost-optimal planning, orbit space search improves A* performance by exploiting symmetry pruning, essentially performing A* in the orbit space instead of state space. In this work, we take a similar approach to top-k planning. We show theoretical equivalence between the goal paths in the state space and in the orbit space, allowing to perform K* search in the orbit space instead, reconstructing plans from the found paths in the orbit space. We prove that our algorithm is sound and complete for top-k planning and empirically show it to achieve state-of-the-art performance, overtaking all existing to date top-k planners. The code is available at https://github.com/IBM/kstar.

In many real-world settings, an autonomous agent may not have sufficient information or sensory capabilities to accomplish its goals, even when they are achievable. In some cases, the needed information can be provided by another agent, but information sharing might be costly due to limited communication bandwidth and other constraints. We address the problem of Helpful Information Sharing (HIS), which focuses on selecting minimal information to reveal to a partially informed agent in order to guarantee it can achieve its goal. We offer a novel compilation of HIS to a classical planning problem, which can be solved efficiently by any off-the-shelf planner. We provide guarantees of optimality for our approach and describe its extensions to maximize robustness and support settings in which the agent needs to decide which sensors to deploy in the environment. We demonstrate the power of our approaches on a set of standard benchmarks as well as on a novel benchmark.

Consider oriented graph nodes requiring periodic visits by a service agent. The agent moves among the nodes and receives a payoff for each completed service task, depending on the time elapsed since the previous visit to a node. We consider the problem of finding a suitable schedule for the agent to maximize its long-run average payoff per time unit. We show that the problem of constructing an epsilon-optimal schedule is PSPACE-hard for every fixed non-negative epsilon, and that there exists an optimal periodic schedule of exponential length. We propose randomized finite-memory (RFM) schedules as a compact description of the agent's strategies and design an efficient algorithm for constructing RFM schedules. Furthermore, we construct deterministic periodic schedules by sampling from RFM schedules.

Planning tasks succinctly represent labeled transition systems, with each ground action corresponding to a label. This granularity, however, is not necessary for solving planning tasks and can be harmful, especially for model-free methods. In order to apply such methods, the label sets are often manually reduced. In this work, we propose automating this manual process. We characterize a valid label reduction for classical planning tasks and propose an automated way of obtaining such valid reductions by leveraging lifted mutex groups. Our experiments show a significant reduction in the action label space size across a wide collection of planning domains. We demonstrate the benefit of our automated label reduction in two separate use cases: improved sample complexity of model-free reinforcement learning algorithms and speeding up successor generation in lifted planning. The code and supplementary material are available at https://github.com/IBM/Parameter-Seed-Set.

We present recursive small-step multi-agent A* (RS-MAA*), an exact algorithm that optimizes the expected reward in decentralized partially observable Markov decision processes (Dec-POMDPs). RS-MAA* builds on multi-agent A* (MAA*), an algorithm that finds policies by exploring a search tree, but tackles two major scalability concerns. First, we employ a modified, small-step variant of the search tree that avoids the double exponential outdegree of the classical formulation. Second, we use a tight and recursive heuristic that we compute on-the-fly, thereby avoiding an expensive precomputation. The resulting algorithm is conceptually simple, yet it shows superior performance on a rich set of standard benchmarks.

Agent decision making using Reinforcement Learning (RL) heavily relies on either a model or simulator of the environment (e.g., moving in an 8x8 maze with three rooms, playing Chess on an 8x8 board). Due to this dependence, small changes in the environment (e.g., positions of obstacles in the maze, size of the board) can severely affect the effectiveness of the policy learned by the agent. To that end, existing work has proposed training RL agents on an adaptive curriculum of environments (generated automatically) to improve performance on out-of-distribution (OOD) test scenarios. Specifically, existing research has employed the potential for the agent to learn in an environment (captured using Generalized Advantage Estimation, GAE) as the key factor to select the next environment(s) to train the agent. However, such a mechanism can select similar environments (with a high potential to learn) thereby making agent training redundant on all but one of those environments. To that end, we provide a principled approach to adaptively identify diverse environments based on a novel distance measure relevant to environment design. We empirically demonstrate the versatility and effectiveness of our method in comparison to multiple leading approaches for unsupervised environment design on three distinct benchmark problems used in literature.

Macro-operators are a common reformulation method in planning that adds high-level operators corresponding to a fixed sequence of primitive operators. We introduce meta-operators, which allow using different sequences of actions in each state. We show how to automatically verify whether a meta-operator is valid, i.e., the represented behavior is always doable. This can be checked at once for all instantiations of the meta-operator and all reachable states via a compilation into Stackelberg planning, a form of adversarial planning. Our results show that meta-operators learned for multiple domains can often express useful high-level behaviors very compactly, improving planners' performance.

We are interested in realistic planning problems to model the behavior of Non-Playable Characters (NPCs) in video games. Search-based action planning, introduced by the game F.E.A.R. in 2005, has an exponential time complexity allowing to control only a dozen NPCs between two frames. A close study of the plans generated in first-person shooters shows that: (1) actions are unary, (2) actions are contextually post-unique and (3) there is no two instances of the same action in an NPC’s plan. By considering (1), (2) and (3) as restrictions, we introduce new classes of problems with the Simplified Action Structure formalism which indeed allow to model realistic problems and whose instances are solvable by a linear-time algorithm. We also experimentally show that our algorithm is capable of managing millions of NPCs per frame.

In this paper we investigate the optimal controller synthesis problem, so that the system under the controller can reach a specified target set while satisfying given constraints. Existing model predictive control (MPC) methods learn from a set of discrete states visited by previous (sub-)optimized trajectories and thus result in computationally expensive mixed-integer nonlinear optimization. In this paper a novel MPC method is proposed based on reach-avoid analysis to solve the controller synthesis problem iteratively. The reach-avoid analysis is concerned with computing a reach-avoid set which is a set of initial states such that the system can reach the target set successfully. It not only provides terminal constraints, which ensure feasibility of MPC, but also expands discrete states in existing methods into a continuous set (i.e., reach-avoid sets) and thus leads to nonlinear optimization which is more computationally tractable online due to the absence of integer variables. Finally, we evaluate the proposed method and make comparisons with state-of-the-art ones based on several examples.

Deep learning is increasingly used to learn policies for planning problems, yet policies represented by neural networks are difficult to interpret, verify and trust. Existing formal approaches to post-hoc explanations provide concise reasons for a single decision made by an ML model. However, understanding planning policies require explaining sequences of decisions. In this paper, we formulate the problem of finding explanations for the sequence of decisions recommended by a learnt policy in a given state. We show that, under certain assumptions, a minimal explanation for a sequence can be computed by solving a number of single decision explanation problems which is linear in the length of the sequence. We present experimental results of our implementation of this approach for ASNet policies for classical planning domains.

Interpretability of reinforcement learning policies is essential for many real-world tasks but learning such interpretable policies is a hard problem. Particularly, rule-based policies such as decision trees and rules lists are difficult to optimize due to their non-differentiability. While existing techniques can learn verifiable decision tree policies, there is no guarantee that the learners generate a policy that performs optimally. In this work, we study the optimization of size-limited decision trees for Markov Decision Processes (MPDs) and propose OMDTs: Optimal MDP Decision Trees. Given a user-defined size limit and MDP formulation, OMDT directly maximizes the expected discounted return for the decision tree using Mixed-Integer Linear Programming. By training optimal tree policies for different MDPs we empirically study the optimality gap for existing imitation learning techniques and find that they perform sub-optimally. We show that this is due to an inherent shortcoming of imitation learning, namely that complex policies cannot be represented using size-limited trees. In such cases, it is better to directly optimize the tree for expected return. While there is generally a trade-off between the performance and interpretability of machine learning models, we find that on small MDPs, depth 3 OMDTs often perform close to optimally.

We study a new online assignment problem, called the Online Task Assignment with Controllable Processing Time. In a bipartite graph, a set of online vertices (tasks) should be assigned to a set of offline vertices (machines) under the known adversarial distribution (KAD) assumption. We are the first to study controllable processing time in this scenario: There are multiple processing levels for each task and higher level brings larger utility but also larger processing delay. A machine can reject an assignment at the cost of a rejection penalty, taken from a pre-determined rejection budget. Different processing levels cause different penalties. We propose the Online Machine and Level Assignment (OMLA) Algorithm to simultaneously assign an offline machine and a processing level to each online task. We prove that OMLA achieves 1/2-competitive ratio if each machine has unlimited rejection budget and Δ/(3Δ-1)- competitive ratio if each machine has an initial rejection budget up to Δ. Interestingly, the competitive ratios do not change under different settings on the controllable processing time and we can conclude that OMLA is "insensitive" to the controllable processing time.

We consider the problem of risk-aware Markov Decision Processes (MDPs) for Safe AI. We introduce a theoretical framework, Extended Markov Ratio Decision Processes (EMRDP), that incorporates risk into MDPs and embeds environment learning into this framework. We propose an algorithm to find the optimal policy for EMRDP with theoretical guarantees. Under a certain monotonicity assumption, this algorithm runs in strongly-polynomial time both in the discounted and expected average reward models. We validate our algorithm empirically on a Grid World benchmark, evaluating its solution quality, required number of steps, and numerical stability. We find its solution quality to be stable under data noising, while its required number of steps grows with added noise. We observe its numerical stability compared to global methods.