Soft Actor-Critic

Reinforcement learning (RL) policies can deteriorate under out-of-distribution (OOD) magnitude shifts. Starting from soft actor-critic (SAC) and its Bayesian Amnesic Piecewise-Robust (BAPR) predecessor, we study the causal-symbolic BAPR (CS-BAPR) family. The practical method combines six training-stabilization settings with alternative actor heads: a Neural Addition Unit (NAU) with a Neural Multiplication Unit (NMU)-inspired quadratic correction, a Kolmogorov-Arnold Network (KAN), or a multilayer perceptron (MLP) with rectified linear unit (ReLU) or hyperbolic-tangent activations.

Soft Actor-Critic (SAC) is widely used for entropy-regularised reinforcement learning with continuous action spaces, and practical implementations perform only a few actor steps towards an evolving target. In this work, we prove convergence guarantees when the target policy arises from policy mirror descent and compare it with the classical Gibbs target. We derive sufficient conditions for the strong convexity and smoothness of the actor objective, characterised by the curvature of the $Q$-function estimate through the Legendre differential operator, and establish an $\mathcal{O}\!\left(N^{-\frac{1}{5}}\right)$ best-iterate finite-time convergence rate up to actor and critic approximation errors. Moreover, the mirror-descent step size $λ$ directly controls the target drift and hence actor tracking error, whereas the analogous Gibbs bound contains a non-vanishing tracking term.

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.

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.

FastSAC-style methods significantly reduce humanoid motion training time but often suffer from notable performance degradation compared with PPO in whole-body tracking tasks. We target this speed-performance gap by introducing LooperMuscle, a composed expert policy learning framework that restores tracking quality while preserving high training efficiency. LooperMuscle combines a semantically structured mixture-of-experts actor, an expert-aware distributional critic, and contribution-routed replay with deferred curriculum scheduling. These three components form a closed training loop in which expert contributions guide data routing, routed data shape value learning, and value gradients in turn refine expert specialization. Empirically, our approach substantially outperforms vanilla FastSAC in motion tracking accuracy while requiring far less wall-clock time than PPO: where FastSAC trains in about 15 minutes but underperforms, and PPO achieves stronger results but requires about 6 hours, LooperMuscle recovers a substantial fraction of the remaining gap to PPO in roughly 45 minutes of simulation training, delivering practical efficiency for rapid policy iteration. The code will be released to benefit the research community at https://loopermuscle.github.io/.

Exploration in sparse-reward long-horizon tasks poses significant challenges for reinforcement learning. To address these challenges, we propose a two-level Hierarchical Reinforcement Learning (HRL) framework. The first level handles high-level strategic planning, while the low-level uses the continuous-control Soft Actor-Critic (SAC) algorithm, and they utilize entropy-regularized policy optimization. The proposed framework was trained and evaluated using the Search-and-Rescue-2 (SAR-2) dataset. HRL-SAC effectively addresses sparse-reward long-horizon search problems characterized by delayed rewards and continuous control, and its outperforming the flat SAC baseline reinforcement learning in terms of success rates, coverage efficiency, and convergence. These findings indicate that hierarchical entropy-regularized policies are a promising solution to tackle long-horizon sparse-reward reinforcement learning tasks.

Parameterized action reinforcement learning has shown strong performance in environments requiring both discrete action selection and continuous parameterization. Prior work established the effectiveness of single-agent actor-critic algorithms - Greedy Actor-Critic (GAC), Soft Actor-Critic (SAC), and Truncated Quantile Critics (TQC) - on benchmark parameterized action tasks, but their extension to multi-agent settings remains largely unexplored. This paper presents a comparative study of shared-experience multi-agent extensions of these algorithms: Multi-Agent Greedy Actor-Critic (MAGAC), Multi-Agent Soft Actor-Critic (MASAC), and Multi-Agent Truncated Quantile Critics (MATQC). Rather than following the centralized training, decentralized execution (CTDE) paradigm, the proposed framework uses multiple independent actor-critic agents that share a replay buffer while maintaining separate policy and value networks. We evaluate the algorithms on the Platform-v0 and Goal-v0 benchmarks against their single-agent counterparts, using three-, five-, and ten-agent configurations to assess scalability. Performance is measured by average evaluation return and training time across ten independent runs, with one-way ANOVA and Tukey HSD post-hoc tests used to assess statistical significance. Results show that the multi-agent framework consistently improves Greedy Actor-Critic performance, while MASAC and MATQC show comparatively modest gains over their single-agent versions. Increasing the number of agents beyond five yields limited additional performance while substantially raising computational cost, particularly for MAGAC. These results highlight a trade-off between learning performance and computational efficiency, offering insight into the scalability of shared-experience multi-agent actor-critic methods for parameterized action reinforcement learning.

Active beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) enables hybrid transmitting and reflecting mode to achieve effective signal amplification and full-space coverage, thus providing a promising solution for blockage-aware uplink offloading in heterogeneous mobile edge computing (MEC) systems. However, practical hybrid mode active BD-RIS are realized by reciprocal devices, which inherently generate cross-sector energy leakage that will reshape the system-level energy-latency tradeoff. This paper studies energy-aware offloading and resource allocation for reciprocal active BD-RIS-assisted heterogeneous MEC, where offloading decisions, CPU/GPU computation allocation, transmit powers, receive processing, and active BD-RIS are tightly coupled. The resulting problem is a high-dimensional mixed integer nonconvex problem and is difficult to solve efficiently by conventional per-instance optimization. To address this challenge, we develop an end-to-end joint optimization framework based on a refined version of the distributional soft actor--critic algorithm, named as DSAC-T. By modeling return distributions rather than only expected values, DSAC-T improves policy stability under reward heterogeneity and feasibility-boundary sensitivity. Compared with other baseline algorithms, DSAC-T achieves the best energy-latency reward, the highest feasibility ratio of 81.67%, and a fast online decision time of 0.0267 s per scenario.

Additive manufacturing process optimization requires precise parameter control to minimize defects such as porosity. Traditional reinforcement learning (RL) approaches using discrete action spaces suffer from slow convergence and susceptibility to local optima, limiting their effectiveness for high-precision manufacturing tasks. This study addresses these limitations by employing a continuous action space combined with a novel architecture that integrates a multi-head attention mechanism with the Soft Actor-Critic (SAC) algorithm. The attention-based feature extractor enhances the agent's ability to capture subtle variations in low-dimensional input features, enabling more effective exploration-exploitation balance for navigating value spaces with local minima. We validate our approach on porosity prediction and process parameter optimization in laser powder bed fusion, demonstrating faster convergence and higher final reward values compared to standard RL methods including DQN, PPO, TD3, and vanilla SAC. The proposed methodology achieves a convergence value of 322.79 within 14 episodes, outperforming existing approaches while maintaining stability throughout training.

We quantify the energy floor -- the minimum achievable cost given action space constraints -- for Soft Actor-Critic (SAC) HVAC control on the sbsim calibrated building simulator. Through minimum-action experiments, we directly measure this floor at USD 35.51/day, dominated by continuous electrical loads (USD 35.44, 99.8%) with negligible gas consumption. The standard SAC baseline, initialized with schedule-policy replay buffer transitions, converges to USD 37.18/day, 4.7% above the floor. We identify buffer initialization as the dominant source of sub-optimality in this scenario: training from an empty buffer reduces cost to USD 35.57/day, eliminating 96% of the gap. Expanding the supply water temperature range by 10 K yields negligible additional savings (USD 0.03/day), and further expansion triggers physical constraint violations. We additionally uncover a discount factor coupling (gamma_eff = 0.891) shrinking the effective planning horizon from 8.3 h to 46 min -- a benchmark-wide issue warranting audit. Systematic ablation across planning horizon, reward weights, and observation enrichment confirms all pre-filled-buffer configurations cluster within 0.7% (USD 37.18--USD 37.42), demonstrating that equipment minimum power -- not algorithmic design -- imposes the binding constraint.

We present a Multi-task Soft Actor-Critic (SAC) Reinforcement Learning framework designed for open-system quantum control across diverse Hamiltonians, which learns optimal pulse sequences while simultaneously discovering problem-specific evolution time T and number of control pulse segments N. Experimental results across 51 Hamiltonian variations demonstrate that the multi-task SAC model is able to generate control pulses that can drive a system, under environment noise, from its initial state to its target state with high fidelities, establishing essential foundations for universal quantum control applicable to realistic noisy quantum devices. Through progressive expansion of the training Hamiltonian set, we investigate if a single multi-task model trained using a given number of sample Hamiltonians can successfully accomplish state-transfer tasks for Hamiltonians drawn from the same Hamiltonian space but not encountered during training. In addition, our Robustness Infidelity Measure (RIM) analysis reveals that SAC trained policies exhibit superior robustness to pulse amplitude perturbations and decoherence rate variations compared to GRAPE-optimized controls.

Proximal Policy Optimization (PPO) has become the de facto standard for training legged robots, thanks to its robustness and scalability in massively parallel simulation environments like IsaacLab. However, its on-policy nature makes it inherently sample-inefficient, preventing its use for continuous adaptation and fine-tuning on real hardware. Soft Actor-Critic (SAC), by contrast, is an off-policy algorithm that can reuse past experience, making it a natural candidate for sim-to-real transfer workflows where the same algorithm can be used both in simulation and for online learning on the real robot. Despite these advantages, SAC has consistently failed to match PPO's empirical performance in massively parallel training settings. This work identifies the root causes of this gap and introduces targeted modifications, covering policy initialization, timeout-aware critic targets, and multi-step return estimation, that enable SAC to train stably at scale. Evaluated across multiple legged robot platforms and diverse locomotion tasks, our approach closes the performance gap with PPO entirely.

Guided Soft Actor-Critic (GSAC) distills knowledge from a privileged full-state teacher to a partial-observation student for autonomous driving, but uses a fixed distillation coefficient lambda regardless of the agent's uncertainty. We present Belief-Aware GSAC (BA-GSAC), which modulates lambda via ensemble disagreement, and use it as a testbed for a systematic empirical study asking: when does adaptive guidance actually help? Evaluating five strategies (fixed lambda in {0.01, 0.1}, adaptive, linear decay, and vanilla SAC) across three POMDP difficulty levels on Highway-Env, we find that preliminary single-seed runs suggest benefits under mild and moderate partial observability, but under severe occlusion (evaluated with 3 seeds for all methods) the adaptive coefficient collapses to lambda_min within about 3K steps. We trace this to an observability blindness phenomenon: because the ensemble predicts partial observations, it achieves low disagreement even under heavy occlusion, modeling what is visible but unable to detect what is missing. We diagnose the root cause and propose an architectural fix (training the ensemble on full-state predictions using the guiding actor's privileged access); while not validated here, we show that even with current limitations, the warmup phase provides measurable stabilization (CV=13.3% vs. 29.8% for constant lambda=0.01). In fact, a simple deterministic linear decay schedule achieves the best severe-POMDP performance across all metrics (mean 116.5, CV=8.9%), suggesting that the scheduling effect, not the ensemble, drives the stability benefit. These findings provide practical guidance for designing uncertainty-aware teacher-student frameworks and highlight ensemble prediction targets as an important design choice.

Mixture policies theoretically offer greater flexibility than unimodal policies in continuous action reinforcement learning, but the practical benefits of this complexity remain elusive. Mixture policies are notably absent from most state-of-the-art algorithms, raising a fundamental question: Is the added representational overhead useful? We show that increased flexibility can theoretically enhance solution quality and entropy robustness. Yet standard algorithms like SAC do not leverage these advantages. A core issue is the lack of a low-variance reparameterization trick for mixtures, a luxury Gaussian policies enjoy. We propose a marginalized reparameterization (MRP) estimator to address this, proving it offers lower variance than the standard likelihood-ratio (LR) approach. Our experiments across Gym MuJoCo, DeepMind Control Suite, and MetaWorld show that MRP mixture policies significantly outperform their LR ones, and reach parity (sometimes better) with Gaussian counterparts. In addition, we do find several cases where MRP mixture policies exhibit clear empirical advantages. In this paper, we provide a clearer understanding of the trade-offs involved, elevating MRP mixture policies from theoretical curiosity to a practical tool.

This paper explores the application of the Soft Actor-Critic (SAC) algorithm within a Distributional Reinforcement Learning setting and introduces an implementation of such algorithm named Cramér-based Distributional Soft Actor-Critic (C-DSAC). The novel approach employs distributional reinforcement learning to represent state-action values, and minimizes the squared Cramér distance for learning the distribution. Empirical results across various robotic benchmarks indicate that our algorithm surpasses the performance of baseline SAC and contemporary distributional methods, with the performance advantage becoming increasingly pronounced in high-complexity environments. To explain the efficiency of the new approach, we conduct an analysis showing that its superior performance is partly due to \textit{confidence-driven} Q-value updates: High-variance target distributions (low confidence in target) lead to more conservative model updates, thereby attenuating the impact of overestimated values. This work deepens the understanding of distributional reinforcement learning, offering insights into the algorithmic mechanisms governing convergence and value estimation.

Constrained Reinforcement Learning (RL) has emerged as a significant research area within RL, where integrating constraints with rewards is crucial for enhancing safety and performance across diverse control tasks. In the context of heating systems in the buildings, optimizing the energy efficiency while maintaining the residents' thermal comfort can be intuitively formulated as a constrained optimization problem. However, to solve it with RL may require large amount of data. Therefore, an accurate and versatile simulator is favored. In this paper, we propose a novel building simulator I4B which provides interfaces for different usages and apply a model-free constrained RL algorithm named constrained Soft Actor-Critic with Linear Smoothed Log Barrier function (CSAC-LB) to the heating optimization problem. Benchmarking against baseline algorithms demonstrates CSAC-LB's efficiency in data exploration, constraint satisfaction and performance.

Industry is moving toward autonomous, network-connected machines that detect and adapt to changing conditions, including hardware faults. Conventional fault-tolerant design duplicates hardware and reroutes control logic; reinforcement learning (RL) offers a learning-based alternative. This paper presents the first systematic comparison of two RL algorithms -- Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC) -- for integrating fault tolerance into control. Beyond algorithm choice, we investigate four knowledge-transfer strategies: retaining or discarding model parameters, and retaining or discarding storage contents. Performance is evaluated in two Gymnasium environments: Ant-v5 and FetchReachDense-v3. Results show rapid, fault-specific recovery with clear trade-offs. In Ant-v5, retaining PPO's parameters boosts early returns and remains the safest choice across all faults, while retaining SAC's parameters yields mixed outcomes. SAC's early performance further depends on whether the replay buffer is retained: beneficial when prior experiences match current dynamics, but harmful when they diverge. In FetchReachDense-v3, discarding both PPO's and SAC's parameters was most effective under sensor corruption. Across tasks, both algorithms recover near-normal performance within minutes in low-dimensional settings and within days in high-dimensional settings, highlighting a clear trade-off between adaptation speed and asymptotic performance. These findings demonstrate that RL can deliver robust fault tolerance and offer practical guidelines.