Reinforcement learning to choose optimizers

No single optimization method is uniformly best for all problems, and the most suitable optimizer choice can change during a run. Existing approaches that change optimizer during execution typically predetermine part of the strategy: the portfolio is restricted to one algorithm class, the switch occurs once at a fixed time, or the frequency of decisions is treated as a hyperparameter rather than a learned one. We introduce "Reinforcement Learning to Choose Optimizers", which formulates the optimization algorithm choice as a sequential decision-making problem. At each decision, a recurrent policy reads the current run state and decides both which optimizer should be used next and for how long. The portfolio includes both gradient-based and derivative-free optimizers, and each switch passes on the current best solution and a representative step size. A context proxy conditions a gating network over expert heads, and training employs a decoupled actor-critic whose return is expressed in the same empirical runtime distribution metric used at evaluation. Training tasks and portfolio are designed jointly so that no optimizer dominates. On unseen problems, the learned policy outperforms every portfolio optimizer at all but the smallest budgets, and it remains robust under distribution shift.

Hypergradient-based Bilevel Reinforcement Learning with Improved Sample Complexity

Bilevel reinforcement learning (RL) is an important framework within the literature of RL that can be used to formalize various categories of problems, such as meta-learning, hierarchical task decomposition, and reinforcement learning from human feedback (RL-HF). Most of the bilevel RL algorithms are either not scalable because of using hypergradient with Hessian, or they suffer from high sample complexity because of using penalty-based approximation methods. In this work, we propose a hypergradient-based bilevel RL algorithm using the optimality of the Boltzmann policy for the entropy regularized discounted RL objective function. Our proposed algorithm is Hessian-free and obtains an iteration complexity of $O(ε^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(ε^{-2})$ under mild regularity conditions. Further, in our convergence analysis, we are able to remove the assumption of the Polyak-Lojasiewicz (PL) condition on the outer-level objective function present in the prior state-of-the-art sample complexity work.

Meta-Learned Reward Shaping for Reinforcement Learning from Human Feedback

Reinforcement Learning from Human Feedback (RLHF) is the standard approach for aligning large language models with human preferences, but its quality is limited by static, task-agnostic reward models. This mismatch leads to sparse learning signals and suboptimal alignment. We introduce MeRLa (Meta-Learned Reward Shaping), a principled framework that meta-learns a task-aware shaping function $Φ(x,y;φ)$ across auxiliary tasks before RLHF training. The learned shaping produces a composite reward that preserves policy optimality while providing task-specific learning signals. Our meta-objective combines task discrimination, entropy regularization, and potential-based conservation for stable convergence. We provide theoretical guarantees for policy invariance, analyze representation drift sensitivity, and formally address incentive misalignment from entropy maximization. Experiments on LLaMA-3-8B across four benchmarks show consistent improvements over PPO, DPO, GRPO, and DAPO, achieving a 90.8% length-controlled win rate on AlpacaEval 2.0 and a score of 9.14 on MT-Bench, with 41% less training instability. MeRLa retains its benefits when combined with process-based and rubric-based enhanced rewards.

Greedy dynamical meta-learning

Gradient descent scales well to large models, but becomes unstable over long time horizons. Gradient-free optimizers can scale to arbitrary timespans, but are hobbled by high dimensions. Since learning occurs in large models over long timescales, neither of these approaches is likely to produce traits which can accelerate the learning process. Instead, we propose a meta-learning algorithm in which the agent learns to modify its own weights and biases. Our algorithm consists of an inner loop, wherein the agent performs some high-dimensional optimization upon itself, and an outer loop, wherein we perform some low-dimensional optimization upon the inner loop. Since the outer loop handles very few parameters, standard zeroth-order methods may be used.

Searching the Space of Feed-Forward Neural-Network Weight-Update Rules with Fixed Depth Symbolic Regression

We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks. Candidate update rules are represented as fixed-depth symbolic expressions over operands derived from common optimizers, including gradient, momentum, adaptive-gradient, and moment-estimate quantities. Across 30 benchmark/neural network combinations, the symbolic regression procedure found an update rule outperforming the best hyperparameter-tuned established optimizer in 25 cases, with an aggregate MSE reduction of 44.47\% over the improved cases. The discovered rules do not all share a single common symbolic form, but many combine adaptive normalization, momentum-like quantities, nonlinear transformations, and rational expressions. These results suggest that symbolic regression can serve as a lightweight mechanism for discovering compact optimizer variants, while also highlighting the need for larger-scale validation.

From Trajectories to Instructions: Language-Conditioned Meta-Reinforcement Learning

Model-Agnostic Meta-Learning (MAML) is a widely used framework for reinforcement learning (RL) that enables efficient transfer by learning global policy parameters that can be rapidly adapted to new tasks. MAML training proceeds in two loops: an inner loop where the global parameters are adapted to task-specific parameters, and an outer loop where these task-specific parameters are evaluated and losses are back-propagated to improve the global parameters. Traditionally, the inner loop adaptation is performed by collecting trajectories from the task environment and applying gradient updates on the empirical expected return, which can be a costly operation. We note that it is the outer loop that drives the actual learning of global parameters, and therefore the inner loop adaptation mechanism need not be restricted to be gradient-based. This observation leads us to ask: Can we replace the inner loop trajectory collection and gradient update with a simpler, task-specific signal? In many practical settings, tasks are naturally accompanied by language instructions. Leveraging these instructions as a direct task-specific signal, we propose LA-MAML (Language Adapted MAML), which modifies the inner loop by adapting the global policy parameters in a single step through a learned embedding of the task instruction, replacing the inner loop trajectory collection and gradient-based updates. Experiments on the BabyAI benchmark demonstrate that LA-MAML achieves competitive or improved performance compared to baselines at a significantly lower per-iteration wall-clock training time. These results demonstrate that language instructions are an effective and efficient substitute for trajectory-based inner loop adaptation in meta RL.

Quasi-Monte Carlo Initialization for Meta-Reinforcement Learning

This paper explores the efficacy of quasi-Monte Carlo (QMC) weight initialization for meta-reinforcement learning within modern benchmark environments. Various sampling methods are used to bound a population-based search and aggregate an optimal prior from a baseline set of tasks. The QMC meta-priors show improvements in training convergence compared to modern orthogonal (SB3) defaults when extrapolated to similar unseen continuous control environments. In dissimilar tasks, the orthogonal orientation was globally superior for an unbiased search.

Knowledge Reutilization in Meta-Reinforcement Learning

Meta-reinforcement learning enables fast adaptation by extracting shared structure from related tasks, but existing end-to-end methods often couple task inference with embodiment-specific control. This coupling can obscure non-parametric task semantics, reduce sample efficiency, and limit cross-agent reuse. We propose a meta-knowledge reutilization framework that learns task-level knowledge on a dynamics-simplified agent and transfers it to heterogeneous agents. The framework uses a Bayesian non-parametric prior to organize latent task modes and a high-level policy to generate task-level magnitude guidance. To bridge reusable task knowledge with different embodiments, we introduce a semantic-magnitude interface and a lightweight temporal adaptor, which convert frozen meta-knowledge into temporally aligned subgoals for embodiment-specific low-level controllers. Experiments on multiple locomotion agents show that our framework reduces final-step tracking error by 94.75% -- 99.79% compared with recent state-of-the-art baselines and achieves comparable deployment performance with about 23.8% of their interaction data.

Nonparametric Learning and Earning with One-Point Feedback under Nonstationarity

Firms increasingly rely on dynamic pricing to respond to evolving customer demand, yet in many applications they observe only the revenue generated by a single posted price in each period. At the same time, market conditions may shift gradually or abruptly due to changes in customer preferences, competition, or external shocks. These features create two intertwined challenges: learning the revenue--demand relationship from limited feedback and adapting pricing decisions to a changing environment. We study how a seller can learn and earn effectively under these constraints, without assuming a specific parametric form for demand. We develop a learning framework that updates prices using revenue-based gradient approximations constructed from one observation per period. To address environmental changes, we incorporate a restarting mechanism that periodically refreshes the learning process so that outdated information is discounted. When the degree of nonstationarity is unknown, we further introduce a meta-learning layer to adaptively hedge across multiple restarting schedules. We provide performance guarantees for our approach, showing how cumulative revenue loss relative to a fully informed benchmark depends on both the time horizon and the magnitude of market variation. Simulation experiments using synthetic and real-world data illustrate the effectiveness of the proposed procedures.

A Meta Reinforcement Learning Approach to Goals-Based Wealth Management

Applying concepts related to zero-shot meta-learning and pre-training of foundation models, we develop a meta reinforcement learning approach (denoted MetaRL) that is pre-trained on thousands of goals-based wealth management (GBWM) problems. Each GBWM problem involves a multiple year scenario over which the investor looks to optimally choose an investment portfolio each year and choose to fulfill all, some, or none of the different financial goals that arise each year. These choices seek to maximize the expected total investor utility obtained from the fulfilled financial goals. By eliminating separate training and optimization for each new investor problem, the MetaRL model in inference mode produces near-optimal dynamic investment portfolio and goal-fulfilling strategies for a new GBWM problem within a few hundredths of a second. This delivers expected utilities that are, on average, 97.8% of the optimal expected utilities (determined via Dynamic Programming). These results are remarkably robust to capital market regime changes, even when training uses only one capital market regime. Further, the MetaRL approach can enable solving problems with larger state spaces where Dynamic Programming becomes computationally infeasible.