Credit assignment in large-language-model reinforcement learning (LLM RL) can be separated into three objects: evidence about success, a transport operator that converts this evidence into token-level advantages, and an update geometry that turns advantages into policy changes. Recent work has greatly improved evidence, sampling, and update geometry, but the transport operator is usually architecture-agnostic. Fixed-discount GAE applies a stationary geometric kernel along token time; group-relative methods broadcast an outcome statistic across an entire response. Neither operator represents the trajectory-specific computation used by the Transformer policy itself. We introduce computation-conditioned credit transport (CCT), a general framework in which a detached statistic of the behavior policy's internal computation parameterizes the causal kernel that transports downstream value through a rollout. Our concrete algorithm, CompPO, maps native attention concentration to a bounded per-token retention gate, uses the gate in both the one-step bootstrap and a path-dependent generalized-advantage trace (Comp-GAE), and co-designs a transport-aligned critic (TAC) that reuses the actor's hidden states and routing information without a second same-scale Transformer. The task reward and clipped PPO policy objective remain unchanged; a constant gate recovers fixed-coefficient GAE. Across five Qwen3-4B seeds, CompPO reaches 61.4% final held-out accuracy (95% CI [60.8,62.0]) versus 53.8% [52.9,54.7] for tuned GRPO. Neither Comp-GAE with a standard critic (55.2%) nor TAC with a fixed gate (56.4%) matches the full model (interaction +2.4 [1.9,2.9]). Shuffle and position controls confirm trajectory-specific alignment; CompPO is stable in 10/12 PPO-grid runs versus 3/12. Frozen evaluation improves over GRPO by 4.3 and 3.9 greedy pass@1 macro points on Qwen3-4B and Llama-3.1-8B-Instruct.
This paper presents an event-driven learning and benchmarking framework for the Dynamic Multi-Depot Vehicle Routing Problem with progressively revealed requests and evolving vehicle states. Masked MLP and Transformer policies are trained through behavior cloning and proximal policy optimization. Deterministic feasibility masking prevents invalid vehicle--request assignments, while fixed-prefix/flexible-suffix route commitments protect completed, active, and near-term decisions and separately measure vehicle reassignment and resequencing. The learned policies are compared with dynamic insertion heuristics and time-limited rolling-horizon optimization. In a 20-scenario policy benchmark, all methods completed every request without invalid actions, but nearest feasible achieved the lowest mean objective and outperformed the learned policies in routing quality, waiting time, stability, makespan, and runtime. Across five independent training runs, PPO had little average effect on the MLP and improved the Transformer on average, although with greater seed variability. Under the common protocol, nearest feasible achieved the lowest combined objective and route disruption, whereas rolling horizon achieved the lowest waiting times and makespan at substantially higher computational cost. The learned policies retained millisecond-level decisions and transferred to instances with up to 80 requests without retraining, but did not outperform the strongest heuristic. No single method was best across routing efficiency, service responsiveness, stability, and online computation.
Faizan Ahmed, Aniket Dixit, James Bruseycs.LG cs.AI
On--off cycling is the main cause of compressor wear in residential heat pumps, yet reinforcement learning (RL) controllers for buildings typically optimise only energy cost and thermal comfort, ignoring how much the learned policy cycles. We add a levelised compressor-wear term to the control reward and study how the resulting behaviour depends on the RL algorithm. Training Soft Actor---Critic (SAC) and Proximal Policy Optimisation (PPO) on an identical Markov decision process for the BOPTEST bestest hydronic heat pump case, we find that SAC learns a continuous modulation policy that keeps the compressor permanently engaged---the operating principle of an inverter-driven heat pump---achieving zero start-ups per day, whereas PPO collapses to bang-bang control that cycles more than the baseline. On the BOPTEST emulator the SAC policy cuts thermal discomfort by up to 90.7% for an 11.5% cost increase, while eliminating all baseline cycling.
Preference-based reinforcement learning (PbRL) for general stochastic MDPs often requires training a reward model. Existing reward-model-free methods are either restricted to bandits or deterministic MDPs, such as DPO or P3O, or use zeroth-order, gradient-free optimization, which in general exhibits a slower convergence rate than gradient-based algorithms. Furthermore, existing reward-model-free preference-based RL algorithms almost exclusively use trajectory-level feedback, which can require significant effort from a human evaluator when trajectories are long. On the other hand, segments are much shorter, so they are easier to compare and evaluate. In this paper, we introduce a novel reward-model-free, critic-free, and gradient-based PbRL algorithm compatible with segment preferences named Segment Pairwise Proximal Policy Optimization (SP3O). SP3O utilizes segment-level preference feedback to construct an accurate policy value difference estimator via off-policy importance sampling, and then uses the estimator to compute the policy gradient via a PPO-type loss function. We provide a theoretical basis for the algorithm and analyze the tradeoff in choosing the segment length. We also evaluate it experimentally against other PbRL/RLHF algorithms in robotic control and LLM finetuning settings to show its improved performance, especially in long-horizon tasks.
Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.
The alignment of Small Language Models (SLMs) in the 70--500M parameter range using reinforcement learning is often considered unstable, though the underlying failure mechanisms have not been systematically investigated. In the State-of-the-Art (SOTA) research, fifteen (model, corpus) configurations were trained using Proximal Policy Optimization (PPO). The experiments included Pythia-70M, 160M, 410M and SmolLM2-135M, 360M on the TinyStories, CNN/DailyMail, and Wikitext-103 corpora. Three reproducible failure modes were identified in small-scale language models: silent LoRA parameter freezing in standard PEFT/TRL pipelines, numerical overflow in importance ratios when using bfloat16, and catastrophic policy collapse due to reward-model error. These issues were addressed using a merge-and-reinitialize adapter technique, float32 precision during PPO updates, and a three-layer safety mechanism comprising reward whitening, importance-ratio guarding, and weight rollback. In this paper, a capacity-headroom hypothesis is proposed, which states that PPO performance at the SLM scale depends on both a fluent supervised model ($\text{PPL}<20$) and a discriminative reward signal, rather than on the number of model parameters. The proposed system converged stably in all experiments and improved preference win rate over the SFT baseline in configurations with a fluent prior and an informative reward signal. Furthermore, it outperformed instruction-tuned baselines while requiring significantly less training data. All checkpoints, preference datasets, and training scripts are publicly released$^§$.
We present a traffic-signal control interface in which a shared graph neural network assigns scores to individual traffic movements. Each junction converts these scores into its own variable-sized set of legal signal phases using a deterministic incidence matrix. Directed corridor nodes provide traffic context, while movement nodes represent controlled input-to-output paths through junctions. Typed mean aggregation produces one scalar per movement; phase definitions and signal timing remain outside the learned network. This makes graph size and junction-specific action count independent of the learned parameter shapes. PPO experiments evaluate the interface on unseen synthetic grid geometries, altered signal coverage, and five heterogeneous city graphs. The policies retained performance across unseen geometries within the synthetic grid family, while changes in signal coverage exposed sensitivity to a signal-coverage distribution shift. A single trained city-policy instance executed across all five city graphs, with heterogeneous outcomes. These results provide feasibility evidence rather than a general estimate of transfer to arbitrary road networks.
This paper presents our system for Task 3 of the CLEF 2026 FinMMEval Lab, which requires daily long, flat, or short trading decisions for Bitcoin (BTC) and Tesla (TSLA) using news and historical market data. We formulate the problem as a discrete-action Markov Decision Process and compare four deep reinforcement learning algorithms: Policy Gradient (PG), Proximal Policy Optimization (PPO), Deep Q-Learning (DQL), and Deep Deterministic Policy Gradient (DDPG). The agents use technical indicators, cyclical calendar encodings, and daily news sentiment scores produced by LLaMA 3.2 1B. To reduce overfitting and align training with the objective of outperforming buy-and-hold, we introduce an alpha reward based on excess market return and randomize episode start dates. Hyperparameters are optimized with Ray Tune over 180 trials per algorithm-asset pair, with early stopping and model selection based on validation Sharpe ratio. On the CLEF Task 3 test set, DDPG achieves the strongest overall performance. DQL was selected a priori for the live endpoint because it obtained the highest validation Sharpe ratio, with selection performed without access to the test period. For TSLA, DDPG and DQL achieve cumulative returns of 54.96% and 52.62%, respectively, compared with 16.45% for buy-and-hold. For BTC, DDPG achieves a positive return of 1.58% while buy-and-hold declines by -34.27%. The results also reveal a substantial validation-to-test generalization gap, highlighting the difficulty of transferring policies selected in bull-market conditions to a bear-market regime.
Reinforcement learning holds significant potential for training large language models (LLMs) to handle multi-turn interactive tasks. However, in long-horizon, multi-turn tasks characterized by sparse outcome rewards, directly training with outcome rewards often results in slow convergence due to the sparsity of signals and the lack of fine-grained feedback. Furthermore, the model may fail to learn successful trajectories that are not sampled during training, thereby limiting its performance. Conversely, while employing customized dense process rewards provides richer signals and accelerates convergence, these surrogate rewards may exhibit potential misalignment with the ground-truth outcome rewards. This inconsistency can bias the training direction and ultimately degrade the model's final performance. In this work, we propose Reward-Swap Policy Optimization (RSPO), a method designed to leverage the rich information from dense process rewards to facilitate training with outcome rewards. By utilizing a reward-swap mechanism, RSPO ensures the diversity of sampled trajectories while guaranteeing consistency between the optimization objective and the true outcome rewards, thereby elevating the performance ceiling of the model. We conduct extensive experiments on two challenging agent benchmarks, WebShop and ALFWorld. By applying our method to various reinforcement learning algorithms, including GRPO, PPO, and GiGPO, we demonstrate that RSPO achieves consistent performance improvements across different baselines and benchmarks.
Ranjit Raut, Aarav Subedi, Sagun Rai +2cs.AI cs.GT
Baghchal is a two-player asymmetric board game with Nepali origins where four tigers are to capture goats and twenty goats desire to keep tigers in immobility. Although Baghchal has a complex structure which is strategic, has perfect information structure, and has cultural meaning, it has not been adequately covered in deep reinforcement learning (RL) literature. This paper gives a systematic exploration of four deep RL solutions Deep Q-Network (DQN), REINFORCE, Proximal Policy Optimization (PPO) and MuZero that are trained on one side of the asymmetric gameplay of Baghchal and then evaluated on the other side. The algorithms are rated based on win rate, draw rate, average captures, training convergence and computational cost. It is experimentally found that MuZero generates the best performance in both tasks, achieving 86 percent win over these Tiger and 62 percent win over these Goat and the ability to do so is due to the model-based planning machine through the Monte Carlo Tree Search. PPO is the most realistic algorithm and is provided to be competitive over both asymmetric tasks with significantly reduced computational costs compared to MuZero. Emergent strategic behavior analysis shows that model-based strategies are optimal over long-horizon planning, whereas value-based counterparts like DQN are more biased up towards the Tiger role owing to the more substantial reward signal.
Actor-critic methods depend on learned critics, but critic quality is often evaluated only indirectly through return, temporal-difference error, or value loss. Critic complexity is introduced as an additional diagnostic and intervention dimension for actor-critic reinforcement learning. The analysis uses spectral effective-rank entropy, a rank-like summary of the singular-value distributions of critic weight matrices, to assess critic model complexity. Across TD3 and PPO experiments, critic complexity is tracked together with return and Monte Carlo value-estimation bias. The results show that critic complexity is measurable throughout training and is systematically associated with training behavior, while also making clear that the relationship is heterogeneous across algorithms, tasks, and hyperparameters. A direct complexity-control intervention is then evaluated by adding a spectral-entropy penalty to the critic loss. This intervention reliably changes the targeted spectral quantity, demonstrating that critic complexity can be controlled rather than only observed. Return effects are treated as task-dependent evidence rather than as a general performance claim, because overall complexity-control results vary.
Rui Wang, Linchao Zhang, Qiang Liu +1eess.SP cs.LG cs.NI
Outer-loop link adaptation (OLLA) is widely deployed in 5G NR to track channel variations, yet its reliance on first-order, single-bit feedback degrades performance significantly under high-mobility and fast-varying channels. This paper presents LOLLA (Learned Outer-Loop Link Adaptation), a deep reinforcement learning framework that replaces the conventional OLLA staircase with a learned, continuous SINR offset conditioned on rich PHY/MAC telemetry inaccessible to OLLA. The offset modulates the SINR-to-MCS lookup table, preserving 3GPP-compliant MCS selection and provably subsuming the conventional OLLA update rule. A Proximal Policy Optimization (PPO) policy trained under a Lagrangian block error rate (BLER) constraint automatically enforces tunable reliability targets from 1% to 15% without manual penalty calibration. The framework is realized as the first closed-loop AI-native control dApp on a GPU-accelerated 5G NR stack, achieving end-to-end control latencies under 500 microseconds. Evaluations under 3GPP TDL channel models demonstrate 15% to 92% throughput gains over OLLA across Doppler frequencies up to 400 Hz, while attaining a Pareto frontier that strictly dominates OLLA across all evaluated reliability targets. The learned policy generalizes to unseen channel models and scales to eight concurrent UEs under shared-resource scheduling. In the uplink formulation, the gNB directly observes decoding outcomes, enabling simulation-to-deployment parity.
Bingxu Liu, Jiashun Liu, Johan Obando-Ceron +5cs.LG cs.AI
While Proximal Policy Optimization (PPO) demonstrates strong performance in stationary settings, we show that its standard optimization paradigm struggles in continual and non-stationary environments. The failure does not stem from insufficient model capacity or overly restrictive clipping. Instead, PPO performs persistent, directionally inefficient local updates, which indicates a lack of geometry-aware guidance for accumulating meaningful behavioral change and ultimately hindering transitions toward new behavior patterns. Although divergence-based regularization introduces partial geometric awareness, its monotonically increasing penalties implicitly discourage large policy deviations, even when such shifts are necessary for effective adaptation. To address this limitation, we propose Gaussian Trust Region Policy Optimization (GTR), which reshapes the trust region using a Gaussian kernel. The resulting constraint is bounded and non-monotonic, providing strong local stability while progressively relaxing under sustained high-advantage updates. To further improve robustness, we introduce a Mixture Gaussian Anchor that adapts to recent policy trajectories, reducing variance induced by stale references. GTR is architecture-agnostic and achieves strong performance across games, simulated robotic control, open-world exploration, and language model post-training. These results demonstrate that geometry-aware trust-region design can be a promising direction for robust reinforcement learning in complex non-stationary environments. Our code is available at https://anonymous.4open.science/r/GTR_demo/README.md.
Deokgyu Yoon, Hyungkyu Kang, Joongkyu Lee +4cs.LG cs.AI
Reinforcement learning with verifiable rewards (RLVR) plays a pivotal role in improving the reasoning ability of large language models. However, widely used PPO surrogate objectives are fundamentally local, as they rely on a local approximation of the exact policy gradient objective. While this approximation improves stability by reducing the variance induced by importance sampling, it also introduces structural bias into the surrogate objective, which must be controlled through trust region mechanisms. In this work, we introduce the $N$-step forward trace, which augments the PPO surrogate objective using the cumulative likelihood ratio of the next $N-1$ tokens. Building on this idea, we propose $N$-Step Forward-Trace Policy Optimization (NFPO), a practical RLVR algorithm that integrates the $N$-step forward trace into the masked policy gradient framework. NFPO provides a continuous bridge between the PPO surrogate objective and the exact policy gradient objective, offering a principled mechanism for controlling the bias-variance trade-off. Our theoretical analysis shows that, with an appropriate choice of $N$, the proposed objective yields a tighter policy-improvement bound than the standard PPO surrogate. Experiments on comprehensive reasoning benchmarks demonstrate that NFPO consistently improves performance, supporting our theoretical findings.
System Neural Diversity (SND) measures behavioral heterogeneity in multi-agent reinforcement learning by averaging pairwise distances over all $\binom{n}{2}$ agent pairs, making each call quadratic in team size. We introduce Graph-SND, which replaces this complete-graph average with a weighted average over the edges of an arbitrary graph $G$. Three regimes follow: $G=K_n$ recovers SND exactly; a fixed sparse $G$ defines a localized diversity measure at $O(|E|)$ cost; and random edge samples yield an unbiased Horvitz-Thompson estimator and a normalized sample mean with $O(1/\sqrt{m})$ concentration in the sampled edge count $m$. For fixed sparse graphs we prove forwarding-index distortion bounds for expanders and a spectral refinement under low-rank distance structure; for random $d$-regular graphs we prove an unconditional probabilistic $\widetilde{\mathcal{O}}(D_{\max}/\sqrt{n})$ bound. On VMAS we verify recovery, unbiasedness, concentration, and wall-clock scaling, with a PettingZoo TVD panel checking non-Gaussian transfer. In a 500-iteration $n=100$ PPO run, Bernoulli-$0.1$ Graph-SND tracks full SND while reducing per-call metric time by about $10\times$, and frozen-policy GPU timing up to $n=500$ follows the predicted $\binom{n}{2}/|E|$ speedup. Random $d$-regular expanders empirically achieve $\mathrm{SND}_{G}^{\mathrm{u}}/\mathrm{SND} \in [0.9987, 1.0013]$ at $Θ(n \log n)$ edges. In DiCo diversity control at $n=50$, Bernoulli-$0.1$ Graph-SND preserves set-point tracking with paired reward differences indistinguishable from zero across nine matched cells while cutting per-call metric cost by ${\sim}9.5\times$. Together, these results show that the SND aggregation bottleneck can be removed without changing the metric's semantics, yielding a drop-in sparse alternative that scales beyond complete-graph SND and supports both passive measurement and closed-loop diversity control.
Proximal Policy Optimization (PPO) dominates deep RL but faces a fundamental dilemma. Its "hard clipping" mechanism discards valuable gradient information from outliers, leading to sample inefficiency. Conversely, removing clipping (as in SPO) exposes optimization to unbounded gradients, causing significant instability and hyperparameter sensitivity. To resolve this, we establish a Unified Trust Region Framework that generalizes existing objectives. Within this framework, we derive Anchored Neighborhood Optimization (ANO) based on a set of design principles. We identify that the failure of standard policy gradients stems from a misapplication of gradient influence on outliers. We propose the Redescending Influence Principle, a paradigm shift from monotonic penalties (SPO) and hard-thresholding (PPO) to dynamic outlier suppression, and prove its necessity for stability in high-variance stochastic optimization. Theoretically, we prove ANO possesses the minimal structural complexity required for robust optimization. Empirically, ANO achieves state-of-the-art performance on MuJoCo benchmarks, significantly outperforming PPO and SPO. Notably, ANO demonstrates superior stability, preventing policy collapse even under aggressive hyperparameters (e.g., learning rates 3x larger than standard) where PPO fails completely.