People, robots, and companies mostly divide time and effort among projects, and shared effort games model people investing resources in public endeavours and sharing the generated values. In linear θ sharing (effort) games, a project’s value is linear in the total contribution, thus modelling predictable, uniform, and scalable activities. The threshold θ for effort defines which contributors win and receive their share, equal share modelling standard salaries, equity-minded projects, etc. Thresholds between 0 and 1 model games such as paper co-authorship and shared assignments, where a minimum positive contribution is required for sharing in the value. We constructively characterise the conditions for the existence of a pure equilibrium for θ ∈ { 0,1 } , and for two-player games with a general threshold, and find the prices of anarchy and stability. We also provide existence and efficiency results for more than two players, and use generalised fictitious play simulations to show when a pure equilibrium exists and what its efficiency is. We propose a method for studying solution concepts by refining a solution concept and finding a large natural subclass of games where the refinement coincides with the original solution concept (Nash, in this case). This means that the original concept narrows down to a more demanding concept on certain games, providing new insights for comparing both concepts. We also prove mixed equilibria always exist and bound their efficiency.

This study investigates scheduling strategies for the stochastic resource-constrained project scheduling problem with maximal time lags (SRCPSP/max). Recent advances in Constraint Programming (CP) and Temporal Networks have re-invoked interest in evaluating the advantages and drawbacks of various proactive and reactive scheduling methods. First, we present a new, CP-based fully proactive method. Second, we show how a reactive approach can be constructed using an online rescheduling procedure. A third contribution is based on partial order schedules and uses Simple Temporal Networks with Uncertainty (STNUs). Our statistical analysis shows that the STNU-based algorithm performs best in terms of solution quality, while also showing good relative offline and online computation time

Abstract Smart “predict, then optimize” (SPO) (Elmachtoub in Manag Sci 68(1): 9–26, 2022) is an end-to-end learning strategy for models that predict parameters in optimization problems. Unlike minimizing mean squared error (MSE) which cares about prediction accuracies, SPO aims to ensure that predictions lead to the best possible decisions. The associated loss function, termed SPO loss , measures the decision’s regret from optimal outcomes with parameter realizations. Existing literature has demonstrated the viability of SPO, however, these studies often focus on classical optimization problems and employ a limited set of models for benchmarking. In this study, we tackled a decision-making task inspired by real-world challenges across a wide range of neural network models. Unlike classical problems, our task requires a unique approach: collaboratively training two models to predict different variables. On top of that, one of the decision variables also affects the feasibility of the decisions, further increasing the complexity. While our implementation validates the benefits of SPO, we were surprised to find that models trained exclusively on SPO loss do not consistently attain the minimum regret. Our further investigation into hyperparameters illustrates that the well-tuned models learned very similar patterns from the feature set, irrespective of whether MSE or SPO loss was used. In other words, the change from MSE to SPO loss in training primarily affected the layer biases. Therefore, to improve the learning efficacy with SPO loss, we propose prioritizing learning feature patterns as the fundamental step. Possible strategies include using specialized neural network layers to capture deeper patterns more effectively or simply warming up by training with MSE. Specifically, a warming-up process is particularly advantageous for model(s) where the outputs are closely tied to constraints, as their prediction accuracy significantly impacts the decision feasibility. The insights are investigated empirically through two real-world trading scenarios. By leveraging datasets with diverse properties, we demonstrate the novelty and generalizability of our investigation.

People want to rely on optimization algorithms for complex decisions but verifying the optimality of the solutions can then become a valid concern, particularly for critical decisions taken by non-experts in optimization. One example is the shortest-path problem on a network, occurring in many contexts from transportation to logistics to telecommunications. While the standard shortest-path problem is both solvable in polynomial time and certifiable by duality, introducing side constraints makes solving and certifying the solutions much harder. We propose a proof system for constrained shortest-path problems, which gives a set of logical rules to derive new facts about feasible solutions. The key trait of the proposed proof system is that it specifically includes high-level graph concepts within its reasoning steps (such as connectivity or path structure), in contrast to, e.g., using linear combinations of model constraints. Thus, using our proof system, we can provide a step-by-step, human-auditable explanation showing that the path given by an external solver cannot be improved. Additionally, to maximize the advantages of this setup, we propose a proof search procedure that specifically aims to find small proofs of this form using a procedure similar to A* search. We evaluate our proof system on constrained shortest path instances generated from real-world road networks and experimentally show that we may indeed derive more interpretable proofs compared to an integer programming approach, in some cases leading to much smaller proofs.

Train routing is sensitive to delays that occur in the network. When a train is delayed, it is imperative that a new plan be found quickly, or else other trains may need to be stopped to ensure safety, potentially causing cascading delays. In this paper, we consider this class of multi-agent planning problems, which we call Multi-Agent Execution Delay Replanning. We show that these can be solved by reducing the problem to an any-start-time safe interval planning problem. When an agent has an any-start-time plan, it can react to a delay by simply looking up the precomputed plan for the delayed start time. We identify crucial real-world problem characteristics like the agent's speed, size, and safety envelope, and extend the any-start-time planning to account for them. Experimental results on real-world train networks show that any-start-time plans are compact and can be computed in reasonable time while enabling agents to instantly recover a safe plan.

In reinforcement learning (RL), different reward functions can define the same optimal policy but result in drastically different learning performance. For some, the agent gets stuck with a suboptimal behavior, and for others, it solves the task efficiently. Choosing a good reward function is hence an extremely important yet challenging problem. In this paper, we explore an alternative approach for using rewards for learning. We introduce max-reward RL, where an agent optimizes the maximum rather than the cumulative reward. Unlike earlier works, our approach works for deterministic and stochastic environments and can be easily combined with state-of-the-art RL algorithms. In the experiments, we study the performance of max-reward RL algorithms in two goal-reaching environments from Gymnasium-Robotics and demonstrate its benefits over standard RL. The code is available at https://github.com/veviurko/To-the-Max.

Multiple Object Tracking (MOT) is a rapidly developing research field that targets precise and reliable tracking of objects. Unfortunately, most available MOT datasets typically contain short video clips only, disregarding the indispensable requirement for adequately capturing substantial long-term variations in real-world scenarios. Long-term MOT poses unique challenges due to changes in both the objects and the environment, which remain relatively unexplored. To fill the gap, we propose a time-lapse image dataset inspired by the growth monitoring of strawberries, dubbed The Growing Strawberries Dataset (GSD). The data was captured hourly by six cameras, covering a span of 16 months in 2021 and 2022. During this time, it encompassed a total of 24 plants in two separate greenhouses. The changes in appearance, weight, and position during the ripening process, along with variations in the illumination during data collection, distinguish the task from previous MOT research. These practical issues resulted in a drastic performance downgrade in the track identification and association tasks of state-of-the-art MOT algorithms. We believe The Growing Strawberries will provide a platform for evaluating such long-term MOT tasks and inspire future research. The dataset is available at https://doi.org/10.4121/e3b31ece-cc88-4638-be10-8ccdd4c5f2f7.v1.

Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue. Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems. However, this only works when an objective can be optimized separately for subtrees. We explore this relationship in detail and show the necessary and sufficient conditions for such separability and generalize previous dynamic programming approaches into a framework that can optimize any combination of separable objectives and constraints. Experiments on five application domains show the general applicability of this framework, while outperforming the scalability of general-purpose solvers by a large margin.

Interpretable and fair machine learning models are required for many applications, such as credit assessment and in criminal justice. Decision trees offer this interpretability, especially when they are small. Optimal decision trees are of particular interest because they offer the best performance possible for a given size. However, state-of-the-art algorithms for fair and optimal decision trees have scalability issues, often requiring several hours to find such trees even for small datasets. Previous research has shown that dynamic programming (DP) performs well for optimizing decision trees because it can exploit the tree structure. However, adding a global fairness constraint to a DP approach is not straightforward, because the global constraint violates the condition that subproblems should be independent. We show how such a constraint can be incorporated by introducing upper and lower bounds on final fairness values for partial solutions of subproblems, which enables early comparison and pruning. Our results show that our model can find fair and optimal trees several orders of magnitude faster than previous methods, and now also for larger datasets that were previously beyond reach. Moreover, we show that with this substantial improvement our method can find the full Pareto front in the trade-off between accuracy and fairness.

In domains such as electric vehicle charging, smart distribution grids and autonomous warehouses, multiple agents share the same resources. When planning the use of these resources, agents need to deal with the uncertainty in these domains. Although several models and algorithms for such constrained multiagent planning problems under uncertainty have been proposed in the literature, it remains unclear when which algorithm can be applied. In this survey we conceptualize these domains and establish a generic problem class based on Markov decision processes. We identify and compare the conditions under which algorithms from the planning literature for problems in this class can be applied: whether constraints are soft or hard, whether agents are continuously connected, whether the domain is fully observable, whether a constraint is momentarily (instantaneous) or on a budget, and whether the constraint is on a single resource or on multiple. Further we discuss the advantages and disadvantages of these algorithms. We conclude by identifying open problems that are directly related to the conceptualized domains, as well as in adjacent research areas.

Resource constraints frequently complicate multi-agent planning problems. Existing algorithms for resource-constrained, multi-agent planning problems rely on the assumption that the constraints are deterministic. However, frequently resource constraints are themselves subject to uncertainty from external influences. Uncertainty about constraints is especially challenging when agents must execute in an environment where communication is unreliable, making on-line coordination difficult. In those cases, it is a significant challenge to find coordinated allocations at plan time depending on availability at run time. To address these limitations, we propose to extend algorithms for constrained multi-agent planning problems to handle stochastic resource constraints. We show how to factorize resource limit uncertainty and use this to develop novel algorithms to plan policies for stochastic constraints. We evaluate the algorithms on a search-and-rescue problem and on a power-constrained planning domain where the resource constraints are decided by nature. We show that plans taking into account all potential realizations of the constraint obtain significantly better utility than planning for the expectation, while causing fewer constraint violations.

The problem of optimally scheduling the charging demand of electric vehicles within the constraints of the electricity infrastructure is called the charge scheduling problem. The models of the charging speed, horizon, and charging demand determine the computational complexity of the charge scheduling problem. We show that for about 20 variants the problem is either in P or weakly NP-hard and dynamic programs exist to compute optimal solutions. About 10 other variants of the problem are strongly NP-hard, presenting a potentially significant obstacle to their use in practical situations of scale. An experimental study establishes up to what parameter values the dynamic programs can determine optimal solutions in a couple of minutes.

Multi-agent planning problems with constraints on global resource consumption occur in several domains. Existing algorithms for solving Multi-agent Markov Decision Processes can compute policies that meet a resource constraint in expectation, but these policies provide no guarantees on the probability that a resource constraint violation will occur. We derive a method to bound constraint violation probabilities using Hoeffding's inequality. This method is applied to two existing approaches for computing policies satisfying constraints: the Constrained MDP framework and a Column Generation approach. We also introduce an algorithm to adaptively relax the bound up to a given maximum violation tolerance. Experiments on a hard toy problem show that the resulting policies outperform static optimal resource allocations to an arbitrary level. By testing the algorithms on more realistic planning domains from the literature, we demonstrate that the adaptive bound is able to efficiently trade off violation probability with expected value, outperforming state-of-the-art planners.

In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate to find an optimal joint policy that maximises joint value. Typical algorithms exploit additive structure in the value function, but in the fully-observable multi-agent MDP (MMDP) setting such structure is not present. We propose a new optimal solver for transition-independent MMDPs, in which agents can only affect their own state but their reward depends on joint transitions. We represent these dependencies compactly in conditional return graphs (CRGs). Using CRGs the value of a joint policy and the bounds on partially specified joint policies can be efficiently computed. We propose CoRe, a novel branch-and-bound policy search algorithm building on CRGs. CoRe typically requires less runtime than available alternatives and finds solutions to previously unsolvable problems.

When multiple independent agents use a limited shared resource, they need to coordinate and thereby their planning problems become coupled. We present a resource assignment strategy that decouples agents using marginal utility cost, allowing them to plan individually. We show that agents converge to an expected cost curve by keeping a history of plans, inspired by fictitious play. This performs slightly better than a state-of-the-art best-response approach and is significantly more scalable than a preallocation Mixed-Integer Linear Programming formulation, providing a good trade-off between performance and quality.

People often have reciprocal habits, almost automatically responding to others' actions. A robot who interacts with humans may also reciprocate, in order to come across natural and be predictable. We aim to facilitate decision support that advises on utility-efficient habits in these interactions. To this end, given a model for reciprocation behavior with parameters that represent habits, we define a game that describes what habit one should adopt to increase the utility of the process. This paper concentrates on two agents. The used model defines that an agent's action is a weighted combination of the other's previous actions (reacting) and either i) her innate kindness, or ii) her own previous action (inertia). In order to analyze what happens when everyone reciprocates rationally, we define a game where an agent may choose her habit, which is either her reciprocation attitude (i or ii), or both her reciprocation attitude and weight. We characterize the Nash equilibria of these games and consider their efficiency. We find that the less kind agents should adjust to the kinder agents to improve both their own utility as well as the social welfare. This constitutes advice on improving cooperation and explains real life phenomena in human interaction, such as the societal benefits from adopting the behavior of the kindest person, or becoming more polite as one grows up.

This paper introduces a novel intention-aware routing system (IARS) for electric vehicles. This system enables vehicles to compute a routing policy that minimizes their expected journey time while considering the policies, or intentions, of other vehicles. Considering such intentions is critical for electric vehicles, which may need to recharge en route and face potentially significant queueing times if other vehicles choose the same charging stations. To address this, the computed routing policy takes into consideration predicted queueing times at the stations, which are derived from the current intentions of other electric vehicles. The efficacy of IARS is demonstrated through simulations using realistic settings based on real data from The Netherlands, including charging station locations, road networks, historical travel times, and journey origin-destination pairs. In these settings, IARS is compared with a number of state-of-the-art benchmark routing algorithms and achieves significantly lower average journey times. In some cases, IARS leads to an over 80% improvement in waiting times at charging stations and a more than 50% reduction in overall journey times.

Renewable power sources such as wind and solar are inflexible in their energy production, which requires demand to rapidly follow supply in order to maintain energy balance. Promising controllable demands are air-conditioners and heat pumps which use electric energy to maintain a temperature at a setpoint. Such Thermostatically Controlled Loads (TCLs) have been shown to be able to follow a power curve using reactive control. In this paper we investigate the use of planning under uncertainty to pro-actively control an aggregation of TCLs to overcome temporary grid imbalance. We present a formal definition of the planning problem under consideration, which we model using the Multi-Agent Markov Decision Process (MMDP) framework. Since we are dealing with hundreds of agents, solving the resulting MMDPs directly is intractable. Instead, we propose to decompose the problem by decoupling the interactions through arbitrage. Decomposition of the problem means relaxing the joint power consumption constraint, which means that joining the plans together can cause overconsumption. Arbitrage acts as a conflict resolution mechanism during policy execution, using the future expected value of policies to determine which TCLs should receive the available energy. We experimentally compare several methods to plan with arbitrage, and conclude that a best response-like mechanism is a scalable approach that returns near-optimal solutions.

This paper proposes a new variant of the task allocation problem, where the agents are connected in a social network and tasks arrive at the agents distributed over the network. We show that the complexity of this problem remains NP -complete. Moreover, it is not approximable within some factor. In contrast to this, we develop an efficient greedy algorithm for this problem. Our algorithm is completely distributed, and it assumes that agents have only local knowledge about tasks and resources. We conduct a broad set of experiments to evaluate the performance and scalability of the proposed algorithm in terms of solution quality and computation time. Three different types of networks, namely small-world, random and scale-free networks, are used to represent various social relationships among agents in realistic applications. The results demonstrate that our algorithm works well and also that it scales well to large-scale applications. In addition we consider the same problem in a setting where the agents holding the resources are self-interested. For this, we show how the optimal algorithm can be used to incentivize these agents to be truthful. However, the efficient greedy algorithm cannot be used in a truthful mechanism, therefore an alternative, cluster-based algorithm is proposed and evaluated.

We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n^2 w_d) time, where w_d is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n^2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(n w_d^2 + n^2 s_d) on general graphs, where s_d

We develop a novel learning algorithm RTI for identifying a deterministic real-time automaton (DRTA) from labeled time-stamped event sequences. The RTI algorithm is based on the current state of the art in deterministic finite-state automaton (DFA) identification, called evidence-driven state-merging (EDSM). In addition to having a DFA structure, a DRTA contains time constraints between occurrences of consecutive events. Although this seems a small difference, we show that the problem of identifying a DRTA is much more difficult than the problem of identifying a DFA: identifying only the time constraints of a DRTA given its DFA structure is already NP-complete. In spite of this additional complexity, we show that RTI is a correct and complete algorithm that converges efficiently (from polynomial time and data) to the correct DRTA in the limit. To the best of our knowledge, this is the first algorithm that can identify a timed automaton model from time-stamped event sequences.A straightforward alternative to identifying DRTAs is to identify a DFA that models time implicitly, i.e., a DFA that uses different states for different points in time. Such a DFA can be identified by first sampling the timed sequences using a fixed frequency, and subsequently applying EDSM to the resulting non-timed event sequences. We evaluate the performance of both RTI and this sampling approach experimentally on artificially generated data. In these experiments RTI outperforms the sampling approach significantly. Thus, we show that if we obtain data from a real-time system, it is easier to identify a DRTA from this data than to identify an equivalent DFA.

We advocate the use of an explicit time representation in syntactic pattern recognition because it can result in more succinct models and easier learning problems. We apply this approach to the real-world problem of learning models for the driving behavior of truck drivers. We discretize the values of onboard sensors into simple events. Instead of the common syntactic pattern recognition approach of sampling the signal values at a fixed rate, we model the time constraints using timed models. We learn these models using the RTI+ algorithm from grammatical inference, and show how to use computational mechanics and a form of semi-supervised classification to construct a real-time automaton classifier for driving behavior. Promising results are shown using this new approach.

Restricting the preferences of the agents by assuming that their utility functions linearly depend on a payment allows for the positive results of the Vickrey auction and the Vickrey-Clarke-Groves mechanism. These results, however, are limited to settings where there is some commonly desired commodity or numeraire--money, shells, beads, etcetera--which is commensurable with utility. We propose a generalization of the Vickrey auction that does not assume that the agents' preferences are quasilinear, but nevertheless retains some of the Vickrey auction's desirable properties. In this auction, a bid can be any alternative, rather than just a monetary offer. As a consequence, the auction is also applicable to situations where there is a fixed budget, or no numeraire is available at all (or it is undesirable to use payments for other reasons)--such as, for example, in the allocation of the task of contributing a module to an open-source project. We show that in two general settings, this qualitative Vickrey auction has a dominant-strategy equilibrium, invariably yields a weakly Pareto efficient outcome in this equilibrium, and is individually rational. In the first setting, the center has a linear preference order over a finite set of alternatives, and in the second setting, the bidders' preferences can be represented by continuous utility functions over a closed metric space of alternatives and the center's utility is equipeaked. The traditional Vickrey auction turns out to be a special case of the qualitative Vickrey auction in this second setting.

Multiagent planning methods are concerned with planning by and for a group of agents. If the agents are self-interested, they may be tempted to lie in order to obtain an outcome that is more rewarding for them. We therefore study the multiagent planning problem from a mechanism design perspective, showing how to incentivise agents to be truthful. We prove that the well-known truthful VCG mechanism is not always truthful in the context of optimal planning, and present a modification to fix this. Finally, we present some (domain-dependent) poly-time planning algorithms using this fix that maintain truthfulness in spite of their non-optimality.