reinforcement learning developers

Abstract: Deep reinforcement learning (RL) is a powerful framework for sequential decision-making. Despite many high-profile successes in recent years, deep RL is known to be brittle. An emerging line of research attributes this brittleness to a loss of plasticity in neural networks. However, plasticity loss has so far been understudied in stochastic environments. We study this interplay systematically, training SAC agents on three DeepMind Control tasks augmented with controlled levels of observation and action noise. We find that plasticity-preserving methods increase learning robustness on the two harder tasks, with their advantage growing as observation noise increases, while combining resets with layer normalization underperforms resets alone at every observation noise level tested. Further, stochasticity can accelerate the loss of plasticity in harder environments, whereas in easier settings noise can act as a regularizer that sustains plasticity. Lastly, plasticity loss is most pronounced in the early stages of training. In the most challenging stochastic settings, TD instability rather than gradual plasticity loss becomes the dominant failure mode.

Abstract: Rubric-based rewards provide fine-grained, interpretable supervision for open-ended reinforcement learning, where holistic scalar rewards struggle to capture multidimensional response quality. Static rubrics can lose discriminative power as the policy distribution evolves, while existing policy--rubric co-evolution methods rely on globally prescribed update schedules that ignore heterogeneous reward informativeness. We introduce RACE, a Reward-Adaptive Co-Evolution framework. At the group level, per-rollout-group training-signal routing classifies groups as informative, diversity-collapsed, or rubric-failed, updating the policy only with informative groups while caching rubric failures. At the phase level, event-triggered phase switching enters rubric optimization upon persistent reward saturation and returns when rubric-reward improvement plateaus. Rubric phases train the generator on cached pairs using a frozen judge and a scale-normalized pairwise-margin reward. Across both levels, online threshold adaptation adjusts routing and switching thresholds through proportional control. Under a unified evaluation protocol, RACE achieves the highest average performance and outperforms the strongest fixed-alternation baseline on all eight tasks, while improving rubric discrimination.

Abstract: Differentiable decision trees (DDTs) support end-to-end optimisation and explicit decision paths, but dense oblique splits can obscure the role of individual input features. We propose the Euclidean-Concentrated Differentiable Decision Tree (EU-DDT), which regularises the relative absolute feature weights at each internal node using their normalised squared Euclidean distance from the uniform distribution. This encourages dominance by a small number of features while retaining probabilistic soft routing. Across five matched random seeds, EU-DDT reduces the mean effective number of features from 8.94 to 1.54 on Wine and from 45.28 to 9.06 on Digits. Mean test accuracy changes from 100.0% to 93.9% on Wine and from 92.3% to 94.6% on Digits, illustrating the dataset-dependent trade-off between concentration and predictive performance. We also use EU-DDT to parameterise a PPO actor with an MLP critic. Two random-seed runs per environment show a consistent qualitative increase in concentration while preserving effective task performance. In representative CartPole-v1 and MiniPacman runs, EU-DDT reaches 100% final evaluation success, while mean node concentration increases from 0.1272 to 0.7179 and from 0.0437 to 0.7237, respectively. These results support EU regularisation as a mechanism for reducing node-level feature complexity; the reinforcement-learning evidence remains preliminary because only two seeds are evaluated.

Abstract: Evolution strategies (ES) update a model by sampling a population of perturbed copies, scoring each one, and moving in the reward-weighted direction of the perturbations. This update is usually presented as an estimate of a smoothed gradient. We present a geometrical interpretation of this update instead. Treat each perturbed model as a particle and its reward as the particle's mass. Before scoring, every particle has the same mass and the population balances at its centroid. Once rewards are assigned, it balances at its reward-weighted center of mass instead. We show that the mean-subtracted ES update is exactly this displacement, scaled by a scalar factor that depends on the mean reward, for any finite population. The physical reading needs nonnegative rewards, which can always be arranged by adding a constant to every reward without changing the update. In the limit of a large population or under antithetic sampling, the centroid sits on the model itself, so ES has an even simpler geometric interpretation: from its current location, the model moves towards the reward-weighted center of mass of its own population. The same picture explains what subtracting the mean reward does: it changes the point from which the displacement is measured, from the model to the sampled centroid. Our contribution is an intuitive, geometric way to visualize an ES update, exact for any finite population.

Abstract: Reverse Kullback-Leibler (KL) distillation has shown empirical promise for training language models, but its statistical guarantees and limits remain poorly understood. In particular, the effects of two design choices remain unclear: Does access to the teacher's full action distribution provide an advantage over observing only the probability it assigns to the sampled action? Must training trajectories come from the student (online distillation), or can teacher-generated trajectories (offline distillation) suffice? Our work takes a first step toward understanding the theory underlying these questions. We study the sample complexity of online reverse-KL distillation under two feedback models: the teacher reveals either its full action distribution or only the probability of the student-generated action. We establish minimax bounds for the former and show that substantially more data may be required for the latter. In contrast, offline reverse-KL distillation can attain the same minimax rate whether the teacher reveals its full distribution or only its probability of the teacher-generated action. The key distinction is that teacher-generated actions themselves reveal the teacher's preferences, while queries at student-selected actions can leave those preferences unobserved. This highlights an additional statistical challenge for online distillation compared to offline distillation. These statistical guarantees do not follow simply from optimizing standard distillation objectives: our lower bounds show that common online objectives can fail when candidates are evaluated only on past student-generated trajectories. We develop trajectory-loss and importance-ratio truncation techniques together with policy-space learning to achieve optimal online distillation guarantees.

Abstract: Most convergence guarantees for iterative stochastic algorithms are stated at a fixed iteration count and do not justify stopping at a data-dependent time. Recent work has constructed anytime-valid envelopes that do, but deterministic envelopes are typically too conservative for practical stopping, and existing data-adaptive ones are derived case-by-case, each coupling a specific algorithm to a specific noise model and boundary construction. This paper provides a general recipe for constructing such anytime-valid data-adaptive boundaries for a large class of iterative algorithms. Performance measures of many of these algorithms satisfy a one-step recursion that reduces the entire error analysis to a single general requirement: time-uniform concentration for predictably weighted sums of noise. We formalize this through a strongly adapted sub-$ψ$ condition, and derive off-the-shelf boundary constructions via continuous and discrete mixtures, stitching, and product betting martingales. We show how these boundaries can be directly coupled with a separate algorithmic analysis that derives the one-step recursion to provide a class of readymade anytime-valid envelopes across diverse settings including stochastic gradient descent (SGD), temporal difference learning, and Bures-Wasserstein SGD. In particular, for SGD, our framework either recovers or significantly sharpens every existing envelope we are aware of. Our constructions come with explicit implementation details and are substantiated by numerical experiments.

Abstract: Flow policies capture rich and diverse action distributions, and fine-tuning them with off-policy RL to improve beyond the demonstrations has drawn growing interest. However, fine-tuning a flow policy against a learned value function is not trivial, because the policy generates its action over many flow steps. Adjoint matching offers a principled way to update the flow model itself by propagating value information from the final action back to each flow step, but it requires a vector--Jacobian product through the policy at every step, a cost that grows with the number of flow steps and the policy size. We observe that the batch-averaged velocity Jacobian of pretrained flow policies concentrates on its diagonal. Motivated by this finding, we derive a closed-form scalar adjoint that scales the value gradient at the final action by the flow time, eliminating the per-step vector--Jacobian products. We further find that controlling the critic's value at policy-generated actions is particularly important under the scalar adjoint. Based on these findings, we propose Q-learning with Scalar Adjoint Matching (SQAM), which combines the scalar adjoint with a value penalty at those actions. SQAM's gains concentrate on the four hardest OGBench domains, where its success rate exceeds that of the strongest baseline in each domain by 18 to 35 percentage points. To test whether SQAM extends to large pretrained policies, we also fine-tune a vision-language-action policy on a real bimanual robot. SQAM improves over supervised fine-tuning on all three tasks.

Abstract: Constant-step stochastic approximation generally has a nonzero stationary mean error that persists under time averaging. This paper studies that error for nonlinear two-timescale recursions driven by an exogenous finite-state Markov chain. Under stated smoothness assumptions and conditions on the stationary distribution, we derive a first-order bias expansion whose error bound remains uniform as the slow step size becomes much smaller than the fast step size. Fast-manifold coordinates keep the associated covariance equation regular in this limit. For fast step $η$ and slow step $\varepsilon$, the expansion reveals a mixed contribution $\varepsilon^2/η$ alongside terms linear in each step size. This dependence matters for bias reduction: along power-law step-size paths, the bias exponents need not be integers, so Richardson--Romberg extrapolation requires weights matched to the path. An exactly solvable nonlinear Markov example verifies the coefficients. We verify localization for temporal-difference learning and compare finite-run extrapolation at equal update budgets. For finite runs, we bound the initialization error of tail averages on both timescales under an additional coupling assumption. In the special case of additive independent noise, signed third-moment cancellation yields a sharper remainder.

Abstract: In this work, we consider decision-focused learning (DFL) for a Markov decision process (MDP), where existing methods differentiate through the KKT conditions of the Bellman equation and require solving a linear system over all state-action pairs, limiting its scalability. We address this by reformulating the MDP as an occupancy measure-based linear program (LP), whose feasible region is induced by predicted dynamics, and we derive a closed-form gradient by identifying the active constraints in the feasible polyhedron via the pivoting algorithm. This occupancy measure-based LP layer raises two challenges: (1) LP's solution gradient is discontinuous when active constraints change, and (2) the LP backward cost still scales with the state size, which is costly for large or continuous state spaces. We address the challenges with an augmented Lagrangian surrogate and smooth the boundary jumps by random row sketching of the constraints, and a learnable soft state-aggregation layer and its function-approximation generalization that scales the LP to large finite and continuous-state MDPs. Across multiple tasks, our methods reach lower regret than KKT-based DFL and two-stage baselines with significantly lower computation cost. The source code for all experiments is available at https://github.com/A-Eshragh/State_Aggregation_Project.

Abstract: The cross-entropy method (CEM) uses world-model scores to select action sequences and fit the distribution sampled in its next iteration. A scoring error can therefore change both the present decision and the candidates considered later. We evaluate these two roles separately. Four types of predictive model generate CEM traces, and every model rescores every saved candidate pool. Executing the same candidates in the environment provides a reference elite set and proposal update. Across twelve independently trained task-seed units on Walker and Cheetah, the pre-specified proposal distance falls from the first to the final CEM iteration in every unit. Proposal widths contract and fitted means separate relative to the remaining search width. Pairwise ranking agreement stays near chance on Walker and declines on Cheetah; elite-set agreement does not improve. This comparison shows greater variation between scorers than between pool sources on Cheetah; Walker has variation in both and in their pairings. We use the original six units to select Random nonlinear for a one-update intervention, without inspecting intervention outcomes. Replacing its first model-ranked update with an environment-ranked update lowers final realised selected-sequence cost in those six units and in six further units held out from the selection.

Abstract: On a single task, deep networks can learn many solutions, depending on their optimizer, training data, architecture, and hyperparameters. Many of these solutions are mode-connected: rather than isolated points in weight space, they are connected by low-loss regions. Yet how their internal computation varies within these regions is unknown. A parallel line of work has identified the degeneracy of neural representations: many networks reach similar training loss with distinct internal structures. However, it is unclear how these solutions are related in weight space. We unify these subfields and show for the first time that many different internal mechanisms exist within a local mode-connected region in weight space. To do so, we introduce Hessian Null Space Continuation (HNC), a scalable method that uses local curvature to traverse regions of weight space that preserve network function, and can be steered toward solutions with specified properties. In RNNs trained on a memory task, HNC reaches drastically different representations and dynamics with maintained behavior. In ImageNet-trained Vision Transformers, HNC finds representations that differ more from the original network than any independently trained model with a different architecture or objective. In reinforcement-learning agents, HNC uncovers a distinct navigation strategy at comparable return and exposes reward hacking in an AI Safety Gridworld. Finally, HNC measures the local geometry of the solution set, showing how model size and task complexity shape its dimension and functional sensitivity. Our results show that a surprisingly large amount of representational diversity exists near a single trained solution, unseen by standard gradient-based optimization. HNC identifies and quantifies this diversity, opening new possibilities for mechanistic understanding of solution spaces and for model merging, editing, and fine-tuning.

Abstract: We propose a novel optimizer for low-rank adaptation (LoRA) that explicitly incorporates the gauge symmetry of low-rank factorization. Our optimizer extends recent matrix optimizers for full-parameter training to the manifold of fixed-rank matrices by interpreting them as normalization under a rotated basis. We show how rotation and normalization can be integrated with the fixed-rank manifold efficiently. Our optimizer converges faster to lower held-out loss and achieves better or comparable downstream performance on both supervised finetuning and reinforcement learning tasks.

Abstract: Finding policies for Markov Decision Processes (MDPs) is a central problem in areas such as Reinforcement Learning and Operations Research. Here, we have to repeatedly choose an action that should be performed by an agent. Depending on the action and the current state of the agent, the agent collects a reward and randomly transitions into a new state. The goal is to maximize the reward in expectation over a finite time horizon of length $H$. We consider a recently introduced variant that generalizes the traditionally additive reward function in the model to a monotone submodular one, which allows for capturing a range of interesting applications. Without the stochastic component, this problem is equivalent to the Submodular Orienteering problem, where the goal is to find an $s$-$t$ walk in a directed graph maximizing a monotone submodular function under a length constraint. We present a novel LP-based algorithm for Submodular Orienteering using ideas from the Sherali-Adams hierarchy and Round-or-Cut. Our guarantees are comparable to the known quasi-polynomial time logarithmic approximation for Submodular Orienteering, but also extend to the setting of Submodular Markov Decision Processes. In the polynomial time regime, we present an $O(n^{\varepsilon})$-approximation (and $O(H^{\varepsilon})$ for Submodular MDPs) for every $\varepsilon >0$, where $n$ is the number of vertices, which was unknown even for Submodular Orienteering. Prior to our work, the best known approximation guarantee for Submodular MDPs had an approximation ratio linear in $H$. Beyond these algorithmic results, our methods reveal a trade-off between the approximation guarantee and the number of previously visited vertices on which an agent conditions its decision.

Abstract: Soft Actor-Critic (SAC) represents a continuous policy as an unbounded Gaussian that is squashed by tanh. The Jacobian of that map is $\partial a/\partial u = 1-a^2$, which vanishes as $|a|\to 1$. A natural concern is that this throttle starves the actor of critic signal exactly where extreme actions (full brake, full throttle) are optimal. We test a minimal intervention that restores the missing signal: one extra term in the actor loss whose gradient on the pre-tanh mean is the detached action-gradient of $Q$, with no gain parameter. On a minimum-time double integrator whose optimum is bang-bang at the action bounds, vanilla SAC already reaches near-optimal return ($-31.6$ vs. a calibrated optimum of $-30.3$) across ten paired seeds. An ungated bypass does saturate the policy (99% of eval steps with $|a|\ge 0.9$) and collapses return to $-195.5$. A gated bypass that fires only on the flat shoulder $|a|\in[0.9,0.999]$ also fails, and does so without leaving a saturated policy. Warm-started MetaDrive fine-tuning shows the same pattern: the bypass does not improve return, and where collision rate falls it is typically traded for out-of-road departures. Auto-tuned entropy coefficient rises against the bypass, which is a push toward the tails. The Jacobian effect is real. Treating it as a bug to be undone is not free, and on the tasks studied here it is not helpful. Saturating a bound is not the same as solving a problem whose optimum lives on that bound.