A reproducible mechanism-level case for direct Bellman risk regression is established and the experiments still needed for state-of-the-art comparison are delimited, establishing a reproducible mechanism-level case for direct Bellman risk regression.
Abstract
Active feature acquisition (AFA) asks which unobserved feature to measure next for each test instance under a budget. Greedy rules are easy to train but can overlook context features whose value is realized only through later acquisitions, while reinforcement-learning and generative approaches introduce difficult optimization or conditional-density estimation. We introduce \method, a deployable, supervised alternative that learns a separate candidate-conditioned risk-to-go function for every remaining budget. Starting from the one-step terminal classification risk, the functions are fitted backward with Bellman targets; inference greedily minimizes the learned terminal risk using only observed values, the mask, candidate identity, and remaining budget. A controlled non-myopic benchmark shows the expected mechanism: at budgets two and three, \method improves accuracy over its one-step ablation by $4.84\pm2.17$ and $4.39\pm1.10$ percentage points (mean $\pm$ standard error over five seeds). On Fashion-MNIST with 20 candidate pixels, it improves accuracy at every nontrivial reported budget on average, including $10.20\pm0.74$ points at four acquisitions; its mean paired gain across budgets $\{2,4,8,12,16\}$ is $3.50\pm0.37$ points. A three-seed MiniBooNE study is mixed at small budgets but positive at 8 and 16 acquisitions, identifying a current boundary rather than supporting a universal claim. These results establish a reproducible mechanism-level case for direct Bellman risk regression and delimit the experiments still needed for state-of-the-art comparison.
Multi-step returns accelerate reward propagation in off-policy reinforcement learning, but couple the evaluation of each decision to the suboptimal logged actions that follow it, inducing a pessimistic bias that grows with the horizon. We propose Expectile $n$-step Q-learning (ENQ), which replaces the symmetric $n$-step temporal-difference (TD) loss with an asymmetric expectile loss on the action-value error, with expectile level $\tau$ as the only method-specific hyperparameter added beyond $n$-step TD. We prove that the ENQ operator is a $\gamma^{n}$-contraction. Under deterministic dynamics, at $\tau=1$, its bias vanishes at the optimal action-value function $Q^*$ on covered in-support pairs, and the corresponding fixed point satisfies the separation-$n$ instance and its multiples of the lower-bound inequality used by Long-Horizon Q-learning (LQL). Under stochastic dynamics, the operator bias admits two-sided bounds with horizon-independent noise constants. Using a single expectile level $\tau=0.8$ and a fixed backup horizon across 27 manipulation and navigation task instances, ENQ is competitive with LQL on aggregate, achieves higher measured training-step throughput in our profiling study, and benefits more from a ten-critic ensemble in a controlled scaling experiment.
Risk-aware Q-learning (RaQL) provides a model-free, two-timescale estimator for dynamic risk objectives, but its finite-budget behavior remains fragile: fixed inner-loop hyperparameters can produce unstable value estimates, persistent Bellman residuals, and inefficient sample reuse. This paper proposes an adaptive training controller for Conditional Value-at-Risk (CVaR) RaQL and evaluates it on a daily Bitcoin trading task. The controller preserves the original CVaR estimator and Bellman fixed point; instead, it redesigns the training procedure through six coordinated mechanisms: per-cell inner-step sizing, outer-rate-matched decay synchronization, a short early correction for the VaR-like inner variable, a coverage-first-then-greedy sample allocation rule, progressive suffix aggregation of mature inner estimates, and data-driven calibration of key scales from online-observable quantities. Across 20 random seeds and 856,000 inner-transition samples, the controller reduces the mean empirical CVaR Bellman residual by approximately 85% relative to the fixed-parameter baseline (MeanBEQ: 1.2202 to 0.1854; MeanBEV: 1.1624 to 0.0535) and maintains stability across CVaR levels, discount factors, and training budgets. On the chronological out-of-sample test set, the learned policy attains a Sharpe ratio of 0.9281 with a maximum drawdown of 6.46% after transaction costs. Although buy-and-hold yields a higher cumulative return (35.43% vs. 23.61%), the adaptive policy achieves far lower volatility (9.57% vs. 47.93%), drawdown, and CVaR loss. These results demonstrate that adaptive finite-budget training design, applied solely to the training procedure without altering the risk objective, can materially improve the reliability and risk-adjusted performance of risk-aware Q-learning in financial applications.
Deep Q-Networks (DQNs) learn value functions through bootstrapped temporal-difference updates, where future returns are approximated using a greedy maximization over next-state action values. While effective, this aggregation rule is inherently sensitive to estimation noise: when Q-values are uncertain, the maximization operator deterministically favors the largest estimate, regardless of its reliability, leading to amplified errors through bootstrapping. In this work, we propose the \textbf{S}uccessor Rollout \textbf{A}ggregation \textbf{D}eep \textbf{Q}-Network (SADQ), a simple modification to Q-learning that regularizes how the TD target is formed. SADQ uses one-step rollout predictions from a learned dynamics model to guide the comparison among candidate next-state actions, introducing additional structure into the aggregation step without altering the underlying learning framework. The resulting mixed Bellman update attenuates unreliable maxima while preserving the standard fixed point under diminishing model error. We provide theoretical analysis showing that SADQ reduces bootstrap-induced overestimation in a pointwise manner. Empirically, SADQ consistently improves training stability across classical control tasks, real-world vector-based environments, and Atari benchmarks when compared to strong DQN variants.
ReBRAC-v2 is introduced, which directly trains an exact-likelihood normalizing flow as the RL actor, combines likelihood, MSE, and MAE behavior regularization, and integrates a classification-based residual critic, staged optimization, and multi-sample test-time action selection, and ranks first in eight categories.
Branch-JEPA is introduced, which replaces this point-valued transition with a context-weighted finite set of latent successors, and preserves more distinct futures, while full-set scoring improves the quality of the resulting predictive distribution.
Zhi Song, Ximing Xing, Zhenchao Tang et al.· 0 citations
Expected-cost constraints can still permit rare, high-cost events. Monte Carlo conditional value at risk (CVaR) gradients can be noisy at high confidence, whereas critics that model an outcome distribution add complexity. We propose BCPPO (Bachelier-Inspired Constrained Proximal Policy Optimization), a proximal policy optimization (PPO) method. Separately initialized cost-prediction networks (critics), trained with random sample masks, produce disagreement that marks predictions sensitive to which state-action regions occur in the training data and to critic training. A Bachelier formula for the expected amount above a reference level converts this disagreement into a smooth policy-update penalty. Gradients from this penalty do not alter the critics, so temporal-difference (TD) critic learning is unchanged. A saturation-aware controller adjusts the mean-cost penalty and stops accumulated error from growing while that penalty is clipped. Deployment retains only the policy network. The disagreement penalty is neither a tail-event probability nor a guaranteed error bound, and it provides no safety guarantee. Across 175 runs with shared tasks, costs, budgets, training steps, and evaluation seeds, no comparator attains both higher mean return and lower mean CVaR than BCPPO in any task. On Push1, BCPPO has no lower return and no higher CVaR than every comparator, with at least one strict gain. These results support a practical balance among reward, caution around cost predictions that vary across trained critics, and policy-only deployment.