The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and InsightsMaxime Gasse, Quentin Cappart, Jonas Charfreitag et al. · deepmind, utoronto
Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning as a new approach for solving combinatorial problems, either directly as solvers or by enhancing exact solvers. Based on this context, the ML4CO aims at improving state-of-the-art combinatorial optimization solvers by replacing key heuristic components. The competition featured three challenging tasks: finding the best feasible solution, producing the tightest optimality certificate, and giving an appropriate solver configuration. Three realistic datasets were considered: balanced item placement, workload apportionment, and maritime inventory routing. This last dataset was kept anonymous for the contestants.
21.3LGNov 4, 2022
Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational BayesMizu Nishikawa-Toomey, Tristan Deleu, Jithendaraa Subramanian et al.
Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.
Task-Agnostic Continual Reinforcement Learning: Gaining Insights and Overcoming ChallengesMassimo Caccia, Jonas Mueller, Taesup Kim et al.
Continual learning (CL) enables the development of models and agents that learn from a sequence of tasks while addressing the limitations of standard deep learning approaches, such as catastrophic forgetting. In this work, we investigate the factors that contribute to the performance differences between task-agnostic CL and multi-task (MTL) agents. We pose two hypotheses: (1) task-agnostic methods might provide advantages in settings with limited data, computation, or high dimensionality, and (2) faster adaptation may be particularly beneficial in continual learning settings, helping to mitigate the effects of catastrophic forgetting. To investigate these hypotheses, we introduce a replay-based recurrent reinforcement learning (3RL) methodology for task-agnostic CL agents. We assess 3RL on a synthetic task and the Meta-World benchmark, which includes 50 unique manipulation tasks. Our results demonstrate that 3RL outperforms baseline methods and can even surpass its multi-task equivalent in challenging settings with high dimensionality. We also show that the recurrent task-agnostic agent consistently outperforms or matches the performance of its transformer-based counterpart. These findings provide insights into the advantages of task-agnostic CL over task-aware MTL approaches and highlight the potential of task-agnostic methods in resource-constrained, high-dimensional, and multi-task environments.
7.7LGJun 2, 2023
Improving the generalizability and robustness of large-scale traffic signal controlTianyu Shi, Francois-Xavier Devailly, Denis Larocque et al.
A number of deep reinforcement-learning (RL) approaches propose to control traffic signals. In this work, we study the robustness of such methods along two axes. First, sensor failures and GPS occlusions create missing-data challenges and we show that recent methods remain brittle in the face of these missing data. Second, we provide a more systematic study of the generalization ability of RL methods to new networks with different traffic regimes. Again, we identify the limitations of recent approaches. We then propose using a combination of distributional and vanilla reinforcement learning through a policy ensemble. Building upon the state-of-the-art previous model which uses a decentralized approach for large-scale traffic signal control with graph convolutional networks (GCNs), we first learn models using a distributional reinforcement learning (DisRL) approach. In particular, we use implicit quantile networks (IQN) to model the state-action return distribution with quantile regression. For traffic signal control problems, an ensemble of standard RL and DisRL yields superior performance across different scenarios, including different levels of missing sensor data and traffic flow patterns. Furthermore, the learning scheme of the resulting model can improve zero-shot transferability to different road network structures, including both synthetic networks and real-world networks (e.g., Luxembourg, Manhattan). We conduct extensive experiments to compare our approach to multi-agent reinforcement learning and traditional transportation approaches. Results show that the proposed method improves robustness and generalizability in the face of missing data, varying road networks, and traffic flows.
14.6LGJul 10, 2022
Challenging Common Assumptions about Catastrophic ForgettingTimothée Lesort, Oleksiy Ostapenko, Diganta Misra et al.
Building learning agents that can progressively learn and accumulate knowledge is the core goal of the continual learning (CL) research field. Unfortunately, training a model on new data usually compromises the performance on past data. In the CL literature, this effect is referred to as catastrophic forgetting (CF). CF has been largely studied, and a plethora of methods have been proposed to address it on short sequences of non-overlapping tasks. In such setups, CF always leads to a quick and significant drop in performance in past tasks. Nevertheless, despite CF, recent work showed that SGD training on linear models accumulates knowledge in a CL regression setup. This phenomenon becomes especially visible when tasks reoccur. We might then wonder if DNNs trained with SGD or any standard gradient-based optimization accumulate knowledge in such a way. Such phenomena would have interesting consequences for applying DNNs to real continual scenarios. Indeed, standard gradient-based optimization methods are significantly less computationally expensive than existing CL algorithms. In this paper, we study the progressive knowledge accumulation (KA) in DNNs trained with gradient-based algorithms in long sequences of tasks with data re-occurrence. We propose a new framework, SCoLe (Scaling Continual Learning), to investigate KA and discover that catastrophic forgetting has a limited effect on DNNs trained with SGD. When trained on long sequences with data sparsely re-occurring, the overall accuracy improves, which might be counter-intuitive given the CF phenomenon. We empirically investigate KA in DNNs under various data occurrence frequencies and propose simple and scalable strategies to increase knowledge accumulation in DNNs.
4.6LGAug 1, 2022
Model-based graph reinforcement learning for inductive traffic signal controlFrançois-Xavier Devailly, Denis Larocque, Laurent Charlin
Most reinforcement learning methods for adaptive-traffic-signal-control require training from scratch to be applied on any new intersection or after any modification to the road network, traffic distribution, or behavioral constraints experienced during training. Considering 1) the massive amount of experience required to train such methods, and 2) that experience must be gathered by interacting in an exploratory fashion with real road-network-users, such a lack of transferability limits experimentation and applicability. Recent approaches enable learning policies that generalize for unseen road-network topologies and traffic distributions, partially tackling this challenge. However, the literature remains divided between the learning of cyclic (the evolution of connectivity at an intersection must respect a cycle) and acyclic (less constrained) policies, and these transferable methods 1) are only compatible with cyclic constraints and 2) do not enable coordination. We introduce a new model-based method, MuJAM, which, on top of enabling explicit coordination at scale for the first time, pushes generalization further by allowing a generalization to the controllers' constraints. In a zero-shot transfer setting involving both road networks and traffic settings never experienced during training, and in a larger transfer experiment involving the control of 3,971 traffic signal controllers in Manhattan, we show that MuJAM, using both cyclic and acyclic constraints, outperforms domain-specific baselines as well as another transferable approach.
20.8AIJul 5, 2025Code
How to Train Your LLM Web Agent: A Statistical DiagnosisDheeraj Vattikonda, Santhoshi Ravichandran, Emiliano Penaloza et al. · mila
LLM-based web agents have recently made significant progress, but much of it has occurred in closed-source systems, widening the gap with open-source alternatives. Progress has been held back by two key challenges: first, a narrow focus on single-step tasks that overlooks the complexity of multi-step web interactions; and second, the high compute costs required to post-train LLM-based web agents. To address this, we present the first statistically grounded study on compute allocation for LLM web-agent post-training. Our approach uses a two-stage pipeline, training a Llama 3.1 8B student to imitate a Llama 3.3 70B teacher via supervised fine-tuning (SFT), followed by on-policy reinforcement learning. We find this process highly sensitive to hyperparameter choices, making exhaustive sweeps impractical. To spare others from expensive trial-and-error, we sample 1,370 configurations and use bootstrapping to estimate effective hyperparameters. Our results show that combining SFT with on-policy RL consistently outperforms either approach alone on both WorkArena and MiniWob++. Further, this strategy requires only 55% of the compute to match the peak performance of pure SFT on MiniWob++, effectively pushing the compute-performance Pareto frontier, and is the only strategy that can close the gap with closed-source models.
15.7LGApr 25, 2025Code
Addressing Concept Mislabeling in Concept Bottleneck Models Through Preference OptimizationEmiliano Penaloza, Tianyue H. Zhang, Laurent Charlin et al.
Concept Bottleneck Models (CBMs) propose to enhance the trustworthiness of AI systems by constraining their decisions on a set of human-understandable concepts. However, CBMs typically assume that datasets contain accurate concept labels-an assumption often violated in practice, which we show can significantly degrade performance (by 25% in some cases). To address this, we introduce the Concept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigates the negative impact of concept mislabeling on CBM performance. We provide an analysis of key properties of the CPO objective, showing it directly optimizes for the concept's posterior distribution, and contrast it against Binary Cross Entropy (BCE), demonstrating that CPO is inherently less sensitive to concept noise. We empirically confirm our analysis by finding that CPO consistently outperforms BCE on three real-world datasets, both with and without added label noise. We make our code available on Github.
Continual Learning via Local Module CompositionOleksiy Ostapenko, Pau Rodriguez, Massimo Caccia et al.
Modularity is a compelling solution to continual learning (CL), the problem of modeling sequences of related tasks. Learning and then composing modules to solve different tasks provides an abstraction to address the principal challenges of CL including catastrophic forgetting, backward and forward transfer across tasks, and sub-linear model growth. We introduce local module composition (LMC), an approach to modular CL where each module is provided a local structural component that estimates a module's relevance to the input. Dynamic module composition is performed layer-wise based on local relevance scores. We demonstrate that agnosticity to task identities (IDs) arises from (local) structural learning that is module-specific as opposed to the task- and/or model-specific as in previous works, making LMC applicable to more CL settings compared to previous works. In addition, LMC also tracks statistics about the input distribution and adds new modules when outlier samples are detected. In the first set of experiments, LMC performs favorably compared to existing methods on the recent Continual Transfer-learning Benchmark without requiring task identities. In another study, we show that the locality of structural learning allows LMC to interpolate to related but unseen tasks (OOD), as well as to compose modular networks trained independently on different task sequences into a third modular network without any fine-tuning. Finally, in search for limitations of LMC we study it on more challenging sequences of 30 and 100 tasks, demonstrating that local module selection becomes much more challenging in presence of a large number of candidate modules. In this setting best performing LMC spawns much fewer modules compared to an oracle based baseline, however, it reaches a lower overall accuracy. The codebase is available under https://github.com/oleksost/LMC.
Sequoia: A Software Framework to Unify Continual Learning ResearchFabrice Normandin, Florian Golemo, Oleksiy Ostapenko et al.
The field of Continual Learning (CL) seeks to develop algorithms that accumulate knowledge and skills over time through interaction with non-stationary environments. In practice, a plethora of evaluation procedures (settings) and algorithmic solutions (methods) exist, each with their own potentially disjoint set of assumptions. This variety makes measuring progress in CL difficult. We propose a taxonomy of settings, where each setting is described as a set of assumptions. A tree-shaped hierarchy emerges from this view, where more general settings become the parents of those with more restrictive assumptions. This makes it possible to use inheritance to share and reuse research, as developing a method for a given setting also makes it directly applicable onto any of its children. We instantiate this idea as a publicly available software framework called Sequoia, which features a wide variety of settings from both the Continual Supervised Learning (CSL) and Continual Reinforcement Learning (CRL) domains. Sequoia also includes a growing suite of methods which are easy to extend and customize, in addition to more specialized methods from external libraries. We hope that this new paradigm and its first implementation can help unify and accelerate research in CL. You can help us grow the tree by visiting www.github.com/lebrice/Sequoia.
Pretraining Representations for Data-Efficient Reinforcement LearningMax Schwarzer, Nitarshan Rajkumar, Michael Noukhovitch et al.
Data efficiency is a key challenge for deep reinforcement learning. We address this problem by using unlabeled data to pretrain an encoder which is then finetuned on a small amount of task-specific data. To encourage learning representations which capture diverse aspects of the underlying MDP, we employ a combination of latent dynamics modelling and unsupervised goal-conditioned RL. When limited to 100k steps of interaction on Atari games (equivalent to two hours of human experience), our approach significantly surpasses prior work combining offline representation pretraining with task-specific finetuning, and compares favourably with other pretraining methods that require orders of magnitude more data. Our approach shows particular promise when combined with larger models as well as more diverse, task-aligned observational data -- approaching human-level performance and data-efficiency on Atari in our best setting. We provide code associated with this work at https://github.com/mila-iqia/SGI.
Beyond Trivial Counterfactual Explanations with Diverse Valuable ExplanationsPau Rodriguez, Massimo Caccia, Alexandre Lacoste et al.
Explainability for machine learning models has gained considerable attention within the research community given the importance of deploying more reliable machine-learning systems. In computer vision applications, generative counterfactual methods indicate how to perturb a model's input to change its prediction, providing details about the model's decision-making. Current methods tend to generate trivial counterfactuals about a model's decisions, as they often suggest to exaggerate or remove the presence of the attribute being classified. For the machine learning practitioner, these types of counterfactuals offer little value, since they provide no new information about undesired model or data biases. In this work, we identify the problem of trivial counterfactual generation and we propose DiVE to alleviate it. DiVE learns a perturbation in a disentangled latent space that is constrained using a diversity-enforcing loss to uncover multiple valuable explanations about the model's prediction. Further, we introduce a mechanism to prevent the model from producing trivial explanations. Experiments on CelebA and Synbols demonstrate that our model improves the success rate of producing high-quality valuable explanations when compared to previous state-of-the-art methods. Code is available at https://github.com/ElementAI/beyond-trivial-explanations.
Online Continual Learning with Maximally Interfered RetrievalRahaf Aljundi, Lucas Caccia, Eugene Belilovsky et al.
Continual learning, the setting where a learning agent is faced with a never ending stream of data, continues to be a great challenge for modern machine learning systems. In particular the online or "single-pass through the data" setting has gained attention recently as a natural setting that is difficult to tackle. Methods based on replay, either generative or from a stored memory, have been shown to be effective approaches for continual learning, matching or exceeding the state of the art in a number of standard benchmarks. These approaches typically rely on randomly selecting samples from the replay memory or from a generative model, which is suboptimal. In this work, we consider a controlled sampling of memories for replay. We retrieve the samples which are most interfered, i.e. whose prediction will be most negatively impacted by the foreseen parameters update. We show a formulation for this sampling criterion in both the generative replay and the experience replay setting, producing consistent gains in performance and greatly reduced forgetting. We release an implementation of our method at https://github.com/optimass/Maximally_Interfered_Retrieval.
Exact Combinatorial Optimization with Graph Convolutional Neural NetworksMaxime Gasse, Didier Chételat, Nicola Ferroni et al.
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs. We train our model via imitation learning from the strong branching expert rule, and demonstrate on a series of hard problems that our approach produces policies that improve upon state-of-the-art machine-learning methods for branching and generalize to instances significantly larger than seen during training. Moreover, we improve for the first time over expert-designed branching rules implemented in a state-of-the-art solver on large problems. Code for reproducing all the experiments can be found at https://github.com/ds4dm/learn2branch.
Language GANs Falling ShortMassimo Caccia, Lucas Caccia, William Fedus et al.
Generating high-quality text with sufficient diversity is essential for a wide range of Natural Language Generation (NLG) tasks. Maximum-Likelihood (MLE) models trained with teacher forcing have consistently been reported as weak baselines, where poor performance is attributed to exposure bias (Bengio et al., 2015; Ranzato et al., 2015); at inference time, the model is fed its own prediction instead of a ground-truth token, which can lead to accumulating errors and poor samples. This line of reasoning has led to an outbreak of adversarial based approaches for NLG, on the account that GANs do not suffer from exposure bias. In this work, we make several surprising observations which contradict common beliefs. First, we revisit the canonical evaluation framework for NLG, and point out fundamental flaws with quality-only evaluation: we show that one can outperform such metrics using a simple, well-known temperature parameter to artificially reduce the entropy of the model's conditional distributions. Second, we leverage the control over the quality / diversity trade-off given by this parameter to evaluate models over the whole quality-diversity spectrum and find MLE models constantly outperform the proposed GAN variants over the whole quality-diversity space. Our results have several implications: 1) The impact of exposure bias on sample quality is less severe than previously thought, 2) temperature tuning provides a better quality / diversity trade-off than adversarial training while being easier to train, easier to cross-validate, and less computationally expensive. Code to reproduce the experiments is available at github.com/pclucas14/GansFallingShort
2.6LGNov 5, 2024
Discovering Data Structures: Nearest Neighbor Search and BeyondOmar Salemohamed, Laurent Charlin, Shivam Garg et al.
We propose a general framework for end-to-end learning of data structures. Our framework adapts to the underlying data distribution and provides fine-grained control over query and space complexity. Crucially, the data structure is learned from scratch, and does not require careful initialization or seeding with candidate data structures/algorithms. We first apply this framework to the problem of nearest neighbor search. In several settings, we are able to reverse-engineer the learned data structures and query algorithms. For 1D nearest neighbor search, the model discovers optimal distribution (in)dependent algorithms such as binary search and variants of interpolation search. In higher dimensions, the model learns solutions that resemble k-d trees in some regimes, while in others, they have elements of locality-sensitive hashing. The model can also learn useful representations of high-dimensional data and exploit them to design effective data structures. We also adapt our framework to the problem of estimating frequencies over a data stream, and believe it could also be a powerful discovery tool for new problems.
Synbols: Probing Learning Algorithms with Synthetic DatasetsAlexandre Lacoste, Pau Rodríguez, Frédéric Branchaud-Charron et al.
Progress in the field of machine learning has been fueled by the introduction of benchmark datasets pushing the limits of existing algorithms. Enabling the design of datasets to test specific properties and failure modes of learning algorithms is thus a problem of high interest, as it has a direct impact on innovation in the field. In this sense, we introduce Synbols -- Synthetic Symbols -- a tool for rapidly generating new datasets with a rich composition of latent features rendered in low resolution images. Synbols leverages the large amount of symbols available in the Unicode standard and the wide range of artistic font provided by the open font community. Our tool's high-level interface provides a language for rapidly generating new distributions on the latent features, including various types of textures and occlusions. To showcase the versatility of Synbols, we use it to dissect the limitations and flaws in standard learning algorithms in various learning setups including supervised learning, active learning, out of distribution generalization, unsupervised representation learning, and object counting.
IG-RL: Inductive Graph Reinforcement Learning for Massive-Scale Traffic Signal ControlFrançois-Xavier Devailly, Denis Larocque, Laurent Charlin
Scaling adaptive traffic-signal control involves dealing with combinatorial state and action spaces. Multi-agent reinforcement learning attempts to address this challenge by distributing control to specialized agents. However, specialization hinders generalization and transferability, and the computational graphs underlying neural-networks architectures -- dominating in the multi-agent setting -- do not offer the flexibility to handle an arbitrary number of entities which changes both between road networks, and over time as vehicles traverse the network. We introduce Inductive Graph Reinforcement Learning (IG-RL) based on graph-convolutional networks which adapts to the structure of any road network, to learn detailed representations of traffic-controllers and their surroundings. Our decentralized approach enables learning of a transferable-adaptive-traffic-signal-control policy. After being trained on an arbitrary set of road networks, our model can generalize to new road networks, traffic distributions, and traffic regimes, with no additional training and a constant number of parameters, enabling greater scalability compared to prior methods. Furthermore, our approach can exploit the granularity of available data by capturing the (dynamic) demand at both the lane and the vehicle levels. The proposed method is tested on both road networks and traffic settings never experienced during training. We compare IG-RL to multi-agent reinforcement learning and domain-specific baselines. In both synthetic road networks and in a larger experiment involving the control of the 3,971 traffic signals of Manhattan, we show that different instantiations of IG-RL outperform baselines.
10.3LGJun 3, 2019
Continual Learning of New Sound Classes using Generative ReplayZhepei Wang, Cem Subakan, Efthymios Tzinis et al.
Continual learning consists in incrementally training a model on a sequence of datasets and testing on the union of all datasets. In this paper, we examine continual learning for the problem of sound classification, in which we wish to refine already trained models to learn new sound classes. In practice one does not want to maintain all past training data and retrain from scratch, but naively updating a model with new data(sets) results in a degradation of already learned tasks, which is referred to as "catastrophic forgetting." We develop a generative replay procedure for generating training audio spectrogram data, in place of keeping older training datasets. We show that by incrementally refining a classifier with generative replay a generator that is 4% of the size of all previous training data matches the performance of refining the classifier keeping 20% of all previous training data. We thus conclude that we can extend a trained sound classifier to learn new classes without having to keep previously used datasets.
11.4LGOct 6, 2017
Learnable Explicit Density for Continuous Latent Space and Variational InferenceChin-Wei Huang, Ahmed Touati, Laurent Dinh et al.
In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its corresponding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and inference. Second, we analyze the family of inverse autoregressive flows (inverse AF) and show that with further improvement, inverse AF could be used as universal approximation to any complicated posterior. Our analysis results in a unified approach to parameterizing a VAE, without the need to restrict ourselves to use factorial Gaussians in the latent real space.
16.8CLMay 18, 2016
On the Evaluation of Dialogue Systems with Next Utterance ClassificationRyan Lowe, Iulian V. Serban, Mike Noseworthy et al.
An open challenge in constructing dialogue systems is developing methods for automatically learning dialogue strategies from large amounts of unlabelled data. Recent work has proposed Next-Utterance-Classification (NUC) as a surrogate task for building dialogue systems from text data. In this paper we investigate the performance of humans on this task to validate the relevance of NUC as a method of evaluation. Our results show three main findings: (1) humans are able to correctly classify responses at a rate much better than chance, thus confirming that the task is feasible, (2) human performance levels vary across task domains (we consider 3 datasets) and expertise levels (novice vs experts), thus showing that a range of performance is possible on this type of task, (3) automated dialogue systems built using state-of-the-art machine learning methods have similar performance to the human novices, but worse than the experts, thus confirming the utility of this class of tasks for driving further research in automated dialogue systems.
27.8MLNov 10, 2014
Deep Exponential FamiliesRajesh Ranganath, Linpeng Tang, Laurent Charlin et al.
We describe \textit{deep exponential families} (DEFs), a class of latent variable models that are inspired by the hidden structures used in deep neural networks. DEFs capture a hierarchy of dependencies between latent variables, and are easily generalized to many settings through exponential families. We perform inference using recent "black box" variational inference techniques. We then evaluate various DEFs on text and combine multiple DEFs into a model for pairwise recommendation data. In an extensive study, we show that going beyond one layer improves predictions for DEFs. We demonstrate that DEFs find interesting exploratory structure in large data sets, and give better predictive performance than state-of-the-art models.
3.8LGJun 18, 2012
Active Learning for Matching ProblemsLaurent Charlin, Rich Zemel, Craig Boutilier
Effective learning of user preferences is critical to easing user burden in various types of matching problems. Equally important is active query selection to further reduce the amount of preference information users must provide. We address the problem of active learning of user preferences for matching problems, introducing a novel method for determining probabilistic matchings, and developing several new active learning strategies that are sensitive to the specific matching objective. Experiments with real-world data sets spanning diverse domains demonstrate that matching-sensitive active learning
19.1AIJun 13, 2012
Hierarchical POMDP Controller Optimization by Likelihood MaximizationMarc Toussaint, Laurent Charlin, Pascal Poupart
Planning can often be simpli ed by decomposing the task into smaller tasks arranged hierarchically. Charlin et al. [4] recently showed that the hierarchy discovery problem can be framed as a non-convex optimization problem. However, the inherent computational di culty of solving such an optimization problem makes it hard to scale to realworld problems. In another line of research, Toussaint et al. [18] developed a method to solve planning problems by maximumlikelihood estimation. In this paper, we show how the hierarchy discovery problem in partially observable domains can be tackled using a similar maximum likelihood approach. Our technique rst transforms the problem into a dynamic Bayesian network through which a hierarchical structure can naturally be discovered while optimizing the policy. Experimental results demonstrate that this approach scales better than previous techniques based on non-convex optimization.