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We propose a novel training regime termed counterfactual training that leverages counterfactual explanations to increase the explanatory capacity of models. Counterfactual explanations have emerged as a popular post-hoc explanation method…

Machine Learning · Computer Science 2026-01-23 Patrick Altmeyer , Aleksander Buszydlik , Arie van Deursen , Cynthia C. S. Liem

Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that…

Systems and Control · Computer Science 2017-07-07 Ernst Moritz Hahn , Vahid Hashemi , Holger Hermanns , Morteza Lahijanian , Andrea Turrini

We consider the verification of multiple expected reward objectives at once on Markov decision processes (MDPs). This enables a trade-off analysis among multiple objectives by obtaining the Pareto front. We focus on strategies that are easy…

Logic in Computer Science · Computer Science 2020-02-18 Florent Delgrange , Joost-Pieter Katoen , Tim Quatmann , Mickael Randour

Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…

Machine Learning · Computer Science 2025-10-03 Aniket Vashishtha , Qirun Dai , Hongyuan Mei , Amit Sharma , Chenhao Tan , Hao Peng

In classical Markov Decision Processes (MDPs), action costs and transition probabilities are assumed to be known, although an accurate estimation of these parameters is often not possible in practice. This study addresses MDPs under cost…

Optimization and Control · Mathematics 2019-06-24 Merve Merakli , Simge Kucukyavuz

Counterfactual explanations are viewed as an effective way to explain machine learning predictions. This interest is reflected by a relatively young literature with already dozens of algorithms aiming to generate such explanations. These…

Machine Learning · Computer Science 2022-12-05 Raphael Mazzine , David Martens

Counterfactual explanations are one of the prominent eXplainable Artificial Intelligence (XAI) techniques, and suggest changes to input data that could alter predictions, leading to more favourable outcomes. Existing counterfactual methods…

Artificial Intelligence · Computer Science 2025-05-22 Andrei Buliga , Chiara Di Francescomarino , Chiara Ghidini , Marco Montali , Massimiliano Ronzani

We consider large-scale Markov decision processes (MDPs) with a risk measure of variability in cost, under the risk-aware MDPs paradigm. Previous studies showed that risk-aware MDPs, based on a minimax approach to handling risk, can be…

Systems and Control · Computer Science 2017-05-17 Pengqian Yu , William B. Haskell , Huan Xu

In this paper titled A Symbolic Approach for Counterfactual Explanations we propose a novel symbolic approach to provide counterfactual explanations for a classifier predictions. Contrary to most explanation approaches where the goal is to…

Artificial Intelligence · Computer Science 2022-06-22 Ryma Boumazouza , Fahima Cheikh-Alili , Bertrand Mazure , Karim Tabia

The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual…

Artificial Intelligence · Computer Science 2025-06-12 Jiri Nemecek , Tomas Pevny , Jakub Marecek

In this paper, we consider reinforcement learning of Markov Decision Processes (MDP) with peak constraints, where an agent chooses a policy to optimize an objective and at the same time satisfy additional constraints. The agent has to take…

Optimization and Control · Mathematics 2019-12-09 Ather Gattami

We study an approach to policy selection for large relational Markov Decision Processes (MDPs). We consider a variant of approximate policy iteration (API) that replaces the usual value-function learning step with a learning step in policy…

Artificial Intelligence · Computer Science 2011-09-13 A. Fern , R. Givan , S. Yoon

We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model dynamics of an agents that operates under resource constraints in a stochastic environment. The presented…

Artificial Intelligence · Computer Science 2021-05-06 František Blahoudek , Petr Novotný , Melkior Ornik , Pranay Thangeda , Ufuk Topcu

Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…

Logic in Computer Science · Computer Science 2026-04-30 Marnix Suilen , Guillermo A. Pérez

We consider a reinforcement learning (RL) setting in which the agent interacts with a sequence of episodic MDPs. At the start of each episode the agent has access to some side-information or context that determines the dynamics of the MDP…

Machine Learning · Statistics 2019-10-24 Aditya Modi , Nan Jiang , Satinder Singh , Ambuj Tewari

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition…

Logic in Computer Science · Computer Science 2018-06-14 Sebastian Arming , Ezio Bartocci , Krishnendu Chatterjee , Joost-Pieter Katoen , Ana Sokolova

Markov decision processes can be viewed as transformers of probability distributions. While this view is useful from a practical standpoint to reason about trajectories of distributions, basic reachability and safety problems are known to…

Logic in Computer Science · Computer Science 2023-05-29 S. Akshay , Krishnendu Chatterjee , Tobias Meggendorfer , Đorđe Žikelić

POMDPs are useful models for systems where the true underlying state is not known completely to an outside observer; the outside observer incompletely knows the true state of the system, and observes a noisy version of the true system…

Machine Learning · Computer Science 2021-09-01 Caleb M. Bowyer

Counterfactual explanations suggest what should be different in the input instance to change the outcome of an AI system. When dealing with counterfactual explanations in the field of Predictive Process Monitoring, however, control flow…

Artificial Intelligence · Computer Science 2025-08-26 Andrei Buliga , Chiara Di Francescomarino , Chiara Ghidini , Ivan Donadello , Fabrizio Maria Maggi

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…

Machine Learning · Computer Science 2026-04-09 David P. Morton , Oscar Dowson , Bernardo K. Pagnoncelli
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