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Yann Ollivier

Publications and source records attributed to Yann Ollivier.

At least 19 recordsLinked to original sources
arXiv2026

Teaching Models to Teach Themselves: Reasoning at the Edge of Learnability

RL methods for scaling large reasoning models stall on datasets with low initial success rates, and thus little training signal. We investigate a fundamental question: Can a pretrained LLM leverage latent knowledge to generate an automated curriculum for problems it cannot solve? We explore this with SOAR: An asymmetric self-play framework that uses meta-RL to surface these pedagogical signals. A teacher model proposes synthetic problems for a student model, and is rewarded with its improvement on a subset of hard problems, thus grounding the curriculum in real student progress rather than intrinsic proxy rewards. Our study on the hardest subsets of math benchmarks (0/128 success) reveals three core findings. First, it is possible to realize bilevel meta-RL that unlocks learning under sparse, binary rewards by sharpening a latent capacity of pretrained models to generate useful problems. Second, grounded rewards outperform intrinsic learnability rewards used in prior LLM self-play, reliably avoiding typical instability and diversity collapse modes. Third, the structure and well-posedness of questions are more critical for learning progress than solution correctness. Our results suggest that the ability to generate useful stepping stones does not require the preexisting ability to solve the hard problems, paving a principled path to escape reasoning plateaus without additional curated data

cs.LG↗
arXiv2026

Likelihood-Based Reward Designs for General LLM Reasoning

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

cs.CL↗
arXiv2025

Soft Tokens, Hard Truths

The use of continuous instead of discrete tokens during the Chain-of-Thought (CoT) phase of reasoning LLMs has garnered attention recently, based on the intuition that a continuous mixture of discrete tokens could simulate a superposition of several reasoning paths simultaneously. Theoretical results have formally proven that continuous tokens have much greater expressivity and can solve specific problems more efficiently. However, practical use of continuous tokens has been limited by strong training difficulties: previous works either just use continuous tokens at inference time on a pre-trained discrete-token model, or must distill the continuous CoT from ground-truth discrete CoTs and face computational costs that limit the CoT to very few tokens. This is the first work introducing a scalable method to learn continuous CoTs via reinforcement learning (RL), without distilling from reference discrete CoTs. We use "soft" tokens: mixtures of tokens together with noise on the input embedding to provide RL exploration. Computational overhead is minimal, enabling us to learn continuous CoTs with hundreds of tokens. On math reasoning benchmarks with Llama and Qwen models up to 8B, training with continuous CoTs match discrete-token CoTs for pass@1 and surpass them for pass@32, showing greater CoT diversity. In systematic comparisons, the best-performing scenario is to train with continuous CoT tokens then use discrete tokens for inference, meaning the "soft" models can be deployed in a standard way. Finally, we show continuous CoT RL training better preserves the predictions of the base model on out-of-domain tasks, thus providing a softer touch to the base model.

cs.CL↗
arXiv2025

Which Features are Best for Successor Features?

In reinforcement learning, universal successor features (SFs) are a way to provide zero-shot adaptation to new tasks at test time: they provide optimal policies for all downstream reward functions lying in the linear span of a set of base features. But it is unclear what constitutes a good set of base features, that could be useful for a wide set of downstream tasks beyond their linear span. Laplacian eigenfunctions (the eigenfunctions of $Δ+Δ^\ast$ with $Δ$ the Laplacian operator of some reference policy and $Δ^\ast$ that of the time-reversed dynamics) have been argued to play a role, and offer good empirical performance. Here, for the first time, we identify the optimal base features based on an objective criterion of downstream performance, in a non-tautological way without assuming the downstream tasks are linear in the features. We do this for three generic classes of downstream tasks: reaching a random goal state, dense random Gaussian rewards, and random ``scattered'' sparse rewards. The features yielding optimal expected downstream performance turn out to be the \emph{same} for these three task families. They do not coincide with Laplacian eigenfunctions in general, though they can be expressed from $Δ$: in the simplest case (deterministic environment and decay factor $γ$ close to $1$), they are the eigenfunctions of $Δ^{-1}+(Δ^{-1})^\ast$. We obtain these results under an assumption of large behavior cloning regularization with respect to a reference policy, a setting often used for offline RL. Along the way, we get new insights into KL-regularized\option{natural} policy gradient, and into the lack of SF information in the norm of Bellman gaps.

cs.LG↗
arXiv2025

Tackling the Zero-Shot Reinforcement Learning Loss Directly

Zero-shot reinforcement learning (RL) methods aim at instantly producing a behavior for an RL task in a given environment, from a description of the reward function. These methods are usually tested by evaluating their average performance on a series of downstream tasks. Yet they cannot be trained directly for that objective, unless the distribution of downstream tasks is known. Existing approaches either use other learning criteria [BBQ+ 18, TRO23, TO21, HDB+ 19], or explicitly set a prior on downstream tasks, such as reward functions given by a random neural network [FPAL24]. Here we prove that the zero-shot RL loss can be optimized directly, for a range of non-informative priors such as white noise rewards, temporally smooth rewards, ``scattered'' sparse rewards, or a combination of those. Thus, it is possible to learn the optimal zero-shot features algorithmically, for a wide mixture of priors. Surprisingly, the white noise prior leads to an objective almost identical to the one in VISR [HDB+19], via a different approach. This shows that some seemingly arbitrary choices in VISR, such as Von Mises--Fisher distributions, do maximize downstream performance. This also suggests more efficient ways to tackle the VISR objective. Finally, we discuss some consequences and limitations of the zero-shot RL objective, such as its tendency to produce narrow optimal features if only using Gaussian dense reward priors.

cs.LG↗
arXiv2024

Finer Behavioral Foundation Models via Auto-Regressive Features and Advantage Weighting

The forward-backward representation (FB) is a recently proposed framework (Touati et al., 2023; Touati & Ollivier, 2021) to train behavior foundation models (BFMs) that aim at providing zero-shot efficient policies for any new task specified in a given reinforcement learning (RL) environment, without training for each new task. Here we address two core limitations of FB model training. First, FB, like all successor-feature-based methods, relies on a linear encoding of tasks: at test time, each new reward function is linearly projected onto a fixed set of pre-trained features. This limits expressivity as well as precision of the task representation. We break the linearity limitation by introducing auto-regressive features for FB, which let finegrained task features depend on coarser-grained task information. This can represent arbitrary nonlinear task encodings, thus significantly increasing expressivity of the FB framework. Second, it is well-known that training RL agents from offline datasets often requires specific techniques.We show that FB works well together with such offline RL techniques, by adapting techniques from (Nair et al.,2020b; Cetin et al., 2024) for FB. This is necessary to get non-flatlining performance in some datasets, such as DMC Humanoid. As a result, we produce efficient FB BFMs for a number of new environments. Notably, in the D4RL locomotion benchmark, the generic FB agent matches the performance of standard single-task offline agents (IQL, XQL). In many setups, the offline techniques are needed to get any decent performance at all. The auto-regressive features have a positive but moderate impact, concentrated on tasks requiring spatial precision and task generalization beyond the behaviors represented in the trainset.

cs.LG↗
arXiv2024

Simple Ingredients for Offline Reinforcement Learning

Offline reinforcement learning algorithms have proven effective on datasets highly connected to the target downstream task. Yet, leveraging a novel testbed (MOOD) in which trajectories come from heterogeneous sources, we show that existing methods struggle with diverse data: their performance considerably deteriorates as data collected for related but different tasks is simply added to the offline buffer. In light of this finding, we conduct a large empirical study where we formulate and test several hypotheses to explain this failure. Surprisingly, we find that scale, more than algorithmic considerations, is the key factor influencing performance. We show that simple methods like AWAC and IQL with increased network size overcome the paradoxical failure modes from the inclusion of additional data in MOOD, and notably outperform prior state-of-the-art algorithms on the canonical D4RL benchmark.

cs.LG↗
arXiv2024

An Equivalence between Bayesian Priors and Penalties in Variational Inference

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference, a tractable way to approximate Bayesian posteriors: the loss to optimize contains a Kullback--Leibler divergence term between the approximate posterior and a Bayesian prior. We fully characterize the regularizers that can arise according to this procedure, and provide a systematic way to compute the prior corresponding to a given penalty. Such a characterization can be used to discover constraints over the penalty function, so that the overall procedure remains Bayesian.

cs.LG↗
arXiv2023

Does Zero-Shot Reinforcement Learning Exist?

A zero-shot RL agent is an agent that can solve any RL task in a given environment, instantly with no additional planning or learning, after an initial reward-free learning phase. This marks a shift from the reward-centric RL paradigm towards "controllable" agents that can follow arbitrary instructions in an environment. Current RL agents can solve families of related tasks at best, or require planning anew for each task. Strategies for approximate zero-shot RL ave been suggested using successor features (SFs) [BBQ+ 18] or forward-backward (FB) representations [TO21], but testing has been limited. After clarifying the relationships between these schemes, we introduce improved losses and new SF models, and test the viability of zero-shot RL schemes systematically on tasks from the Unsupervised RL benchmark [LYL+21]. To disentangle universal representation learning from exploration, we work in an offline setting and repeat the tests on several existing replay buffers. SFs appear to suffer from the choice of the elementary state features. SFs with Laplacian eigenfunctions do well, while SFs based on auto-encoders, inverse curiosity, transition models, low-rank transition matrix, contrastive learning, or diversity (APS), perform unconsistently. In contrast, FB representations jointly learn the elementary and successor features from a single, principled criterion. They perform best and consistently across the board, reaching 85% of supervised RL performance with a good replay buffer, in a zero-shot manner.

cs.LG↗
arXiv2022

Agnostic Physics-Driven Deep Learning

This work establishes that a physical system can perform statistical learning without gradient computations, via an Agnostic Equilibrium Propagation (Aeqprop) procedure that combines energy minimization, homeostatic control, and nudging towards the correct response. In Aeqprop, the specifics of the system do not have to be known: the procedure is based only on external manipulations, and produces a stochastic gradient descent without explicit gradient computations. Thanks to nudging, the system performs a true, order-one gradient step for each training sample, in contrast with order-zero methods like reinforcement or evolutionary strategies, which rely on trial and error. This procedure considerably widens the range of potential hardware for statistical learning to any system with enough controllable parameters, even if the details of the system are poorly known. Aeqprop also establishes that in natural (bio)physical systems, genuine gradient-based statistical learning may result from generic, relatively simple mechanisms, without backpropagation and its requirement for analytic knowledge of partial derivatives.

cs.LG↗
arXiv2021

Learning One Representation to Optimize All Rewards

We introduce the forward-backward (FB) representation of the dynamics of a reward-free Markov decision process. It provides explicit near-optimal policies for any reward specified a posteriori. During an unsupervised phase, we use reward-free interactions with the environment to learn two representations via off-the-shelf deep learning methods and temporal difference (TD) learning. In the test phase, a reward representation is estimated either from observations or an explicit reward description (e.g., a target state). The optimal policy for that reward is directly obtained from these representations, with no planning. We assume access to an exploration scheme or replay buffer for the first phase. The corresponding unsupervised loss is well-principled: if training is perfect, the policies obtained are provably optimal for any reward function. With imperfect training, the sub-optimality is proportional to the unsupervised approximation error. The FB representation learns long-range relationships between states and actions, via a predictive occupancy map, without having to synthesize states as in model-based approaches. This is a step towards learning controllable agents in arbitrary black-box stochastic environments. This approach compares well to goal-oriented RL algorithms on discrete and continuous mazes, pixel-based MsPacman, and the FetchReach virtual robot arm. We also illustrate how the agent can immediately adapt to new tasks beyond goal-oriented RL.

cs.LG↗
arXiv2021

Unbiased Methods for Multi-Goal Reinforcement Learning

In multi-goal reinforcement learning (RL) settings, the reward for each goal is sparse, and located in a small neighborhood of the goal. In large dimension, the probability of reaching a reward vanishes and the agent receives little learning signal. Methods such as Hindsight Experience Replay (HER) tackle this issue by also learning from realized but unplanned-for goals. But HER is known to introduce bias, and can converge to low-return policies by overestimating chancy outcomes. First, we vindicate HER by proving that it is actually unbiased in deterministic environments, such as many optimal control settings. Next, for stochastic environments in continuous spaces, we tackle sparse rewards by directly taking the infinitely sparse reward limit. We fully formalize the problem of multi-goal RL with infinitely sparse Dirac rewards at each goal. We introduce unbiased deep Q-learning and actor-critic algorithms that can handle such infinitely sparse rewards, and test them in toy environments.

cs.LG↗
arXiv2021

Learning Successor States and Goal-Dependent Values: A Mathematical Viewpoint

In reinforcement learning, temporal difference-based algorithms can be sample-inefficient: for instance, with sparse rewards, no learning occurs until a reward is observed. This can be remedied by learning richer objects, such as a model of the environment, or successor states. Successor states model the expected future state occupancy from any given state for a given policy and are related to goal-dependent value functions, which learn how to reach arbitrary states. We formally derive the temporal difference algorithm for successor state and goal-dependent value function learning, either for discrete or for continuous environments with function approximation. Especially, we provide finite-variance estimators even in continuous environments, where the reward for exactly reaching a goal state becomes infinitely sparse. Successor states satisfy more than just the Bellman equation: a backward Bellman operator and a Bellman-Newton (BN) operator encode path compositionality in the environment. The BN operator is akin to second-order gradient descent methods and provides the true update of the value function when acquiring more observations, with explicit tabular bounds. In the tabular case and with infinitesimal learning rates, mixing the usual and backward Bellman operators provably improves eigenvalues for asymptotic convergence, and the asymptotic convergence of the BN operator is provably better than TD, with a rate independent from the environment. However, the BN method is more complex and less robust to sampling noise. Finally, a forward-backward (FB) finite-rank parameterization of successor states enjoys reduced variance and improved samplability, provides a direct model of the value function, has fully understood fixed points corresponding to long-range dependencies, approximates the BN method, and provides two canonical representations of states as a byproduct.

cs.LG↗
arXiv2021

Convergence of Online Adaptive and Recurrent Optimization Algorithms

We prove local convergence of several notable gradient descent algorithms used in machine learning, for which standard stochastic gradient descent theory does not apply directly. This includes, first, online algorithms for recurrent models and dynamical systems, such as \emph{Real-time recurrent learning} (RTRL) and its computationally lighter approximations NoBackTrack and UORO; second, several adaptive algorithms such as RMSProp, online natural gradient, and Adam with $β^2\to 1$.Despite local convergence being a relatively weak requirement for a new optimization algorithm, no local analysis was available for these algorithms, as far as we knew. Analysis of these algorithms does not immediately follow from standard stochastic gradient (SGD) theory. In fact, Adam has been proved to lack local convergence in some simple situations \citep{j.2018on}. For recurrent models, online algorithms modify the parameter while the model is running, which further complicates the analysis with respect to simple SGD.Local convergence for these various algorithms results from a single, more general set of assumptions, in the setup of learning dynamical systems online. Thus, these results can cover other variants of the algorithms considered.We adopt an "ergodic" rather than probabilistic viewpoint, working with empirical time averages instead of probability distributions. This is more data-agnostic and creates differences with respect to standard SGD theory, especially for the range of possible learning rates. For instance, with cycling or per-epoch reshuffling over a finite dataset instead of pure i.i.d.\ sampling with replacement, empirical averages of gradients converge at rate $1/T$ instead of $1/\sqrt{T}$ (cycling acts as a variance reduction method), theoretically allowing for larger learning rates than in SGD.

math.DS↗
arXiv2019

White-box vs Black-box: Bayes Optimal Strategies for Membership Inference

Membership inference determines, given a sample and trained parameters of a machine learning model, whether the sample was part of the training set. In this paper, we derive the optimal strategy for membership inference with a few assumptions on the distribution of the parameters. We show that optimal attacks only depend on the loss function, and thus black-box attacks are as good as white-box attacks. As the optimal strategy is not tractable, we provide approximations of it leading to several inference methods, and show that existing membership inference methods are coarser approximations of this optimal strategy. Our membership attacks outperform the state of the art in various settings, ranging from a simple logistic regression to more complex architectures and datasets, such as ResNet-101 and Imagenet.

stat.ML↗
arXiv2019

First-order Adversarial Vulnerability of Neural Networks and Input Dimension

Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisingly, vulnerability does not depend on network topology: for many standard network architectures, we prove that at initialization, the $\ell_1$-norm of these gradients grows as the square root of the input dimension, leaving the networks increasingly vulnerable with growing image size. We empirically show that this dimension dependence persists after either usual or robust training, but gets attenuated with higher regularization.

stat.ML↗
arXiv2019

Separating value functions across time-scales

In many finite horizon episodic reinforcement learning (RL) settings, it is desirable to optimize for the undiscounted return - in settings like Atari, for instance, the goal is to collect the most points while staying alive in the long run. Yet, it may be difficult (or even intractable) mathematically to learn with this target. As such, temporal discounting is often applied to optimize over a shorter effective planning horizon. This comes at the risk of potentially biasing the optimization target away from the undiscounted goal. In settings where this bias is unacceptable - where the system must optimize for longer horizons at higher discounts - the target of the value function approximator may increase in variance leading to difficulties in learning. We present an extension of temporal difference (TD) learning, which we call TD($Δ$), that breaks down a value function into a series of components based on the differences between value functions with smaller discount factors. The separation of a longer horizon value function into these components has useful properties in scalability and performance. We discuss these properties and show theoretic and empirical improvements over standard TD learning in certain settings.

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