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SpikeCredit: Temporal Credit Carrier for Reinforcement Learning with Sparse Rewards

Yingchao Yu, Pengfei Sun, Wenxuan Pan, Wei Chen, Yitian Hong, Kuangrong Hao, Yaochu Jin

arXiv:2609.35268v1cs.LG

TL;DR

Sparse rewards leave delayed outcomes with little guidance about which intermediate behavior caused success or failure, and delayed outcomes alone cannot recover information not preserved in policy dynamics. SpikeCredit selects spiking temporal credit carriers and couples credit reading with writing recovered targets back into the actor. Across four sparse-reward MuJoCo tasks, it consistently outperforms sparse-reward ANN and SNN baselines.

  • Problem

    Delayed sparse-reward outcomes provide little guidance about which intermediate behavior caused success or failure, and cannot recover transition information that policy dynamics or interaction history did not preserve.

    Source: Introduction · pp. 1–2

  • Method

    SpikeCredit selects membrane traces or spike events as temporal credit carriers, then uses SMF to read transition-level credit and CTT to write recovered targets back into the actor.

    Source: Introduction · p. 2

  • Results

    Across four sparse-reward MuJoCo tasks, SpikeCredit consistently outperforms sparse-reward ANN and SNN baselines, while mechanistic analyses report meaningful alignment with dense-reward structure.

    Source: Introduction · p. 2, Conclusion · p. 7

  • Takeaways & Limitations

    The results support treating spiking dynamics as temporal credit carriers within a closed read-write loop for sparse-reward RL.

    Source: Conclusion · p. 7

    The considered setting provides no intermediate rewards and only a terminal trajectory-level outcome.

    Source: Sparse-Reward RL · p. 3

Abstract

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Reinforcement learning (RL) with sparse rewards is challenging because delayed outcomes provide little guidance about which intermediate computations caused success or failure. We argue that reliable credit assignment requires policy dynamics that preserve and expose credit-relevant information over time, a role we formalize as Temporal Credit Carriers (TCCs) and that spiking neural networks (SNNs) naturally fulfill through graded membrane traces and event-driven spikes. Based on this hypothesis, we propose SpikeCredit, an SNN-based framework for RL with sparse rewards that first performs task-adaptive TCC selection and then closes the loop between a fast TCC-reading pathway, where self-motion feedback constraint uses local behavior-grounded cues to constrain transition-level credit recovery, and a slow TCC-writing pathway, where credit-targeted trace alignment feeds recovered credit back into the actor to make future TCC dynamics more credit-readable. Across sparse-reward MuJoCo tasks, SpikeCredit improves Last10 return over sparse SNN baselines by +1169% on Ant, +953% on Hopper, +723% on Swimmer, and +1781% on Walker2d, and exceeds the dense-reward baseline on Swimmer by +113%. Mechanistic analyses further show substantially stronger alignment with dense rewards than the sparse SNN baseline. These results position spiking dynamics as credit-preserving substrates for sparse-reward RL.

Introduction

Sparse rewards leave delayed outcomes with little guidance for assigning credit to intermediate behavior. SpikeCredit treats spiking policy dynamics as temporal credit carriers and couples task-adaptive carrier selection with credit reading and writing.

Introduction

  • Delayed outcomes provide little guidance about which intermediate states, actions, or computations caused success or failure, making temporal credit assignment difficult.The resulting weak learning signal impedes exploration and requires learning signals to propagate across long temporal distances.Source: Introduction · p. 1
  • Delayed outcomes alone cannot recover transition-level information that the policy or interaction history did not preserve, motivating the question of where credit-relevant temporal information resides.This shifts the focus from only redistributing outcomes to identifying the preserved information needed for reliable redistribution.Source: Introduction · p. 2
  • Temporal Credit Carriers (TCCs) are neural states whose evolution preserves information that can later support transition-level credit inference from delayed outcomes.Membrane potentials provide graded traces of slowly evolving dependencies, while spikes may expose event-specific temporal evidence.Source: Introduction · p. 2
  • SpikeCredit selects membrane traces or spike events according to task temporal characteristics, then reads credit from current dynamics and writes recovered signals back to shape future dynamics.A suitable carrier must preserve temporal information and make it readable for delayed inference and adaptable through learning.Source: Introduction · p. 2
  • The fast SMF pathway uses local behavior-grounded cues to constrain credit inference, while the slow CTT pathway feeds recovered targets back to shape future TCC dynamics.The updated dynamics are reused by SMF in subsequent episodes, forming a read-write loop.Source: Introduction · p. 2
  • Experiments on four sparse-reward MuJoCo tasks show consistent gains over sparse-reward ANN and SNN baselines, with mechanistic analyses and ablations examining dense-reward alignment and component roles.The analyses report meaningful alignment with dense-reward structure and examine carrier selection, SMF, and CTT.Source: Introduction · p. 2

Related Work

Prior sparse-reward methods construct denser supervision or redistribute delayed outcomes, while SpikeCredit focuses on whether policy dynamics preserve credit-relevant information. In spiking RL, it uses membrane and spike temporal characteristics for sparse-reward credit assignment.

Sparse-Reward RL

  • SpikeCredit focuses on whether internal policy dynamics contain credit-relevant information, selecting a task-adaptive carrier and refining its dynamics through a closed credit read-write loop.This contrasts with approaches centered on exploration bonuses or standalone reward redistribution.Source: Sparse-Reward RL · p. 2

Spiking RL

  • SpikeCredit’s overview combines task-statistics-based carrier selection with SMF credit reading and CTT target writing to improve future TCC readability.The selected carrier is membrane- or spike-based.Source: Figure 2 · p. 3
  • Prior spiking RL work addresses learning, representation, stabilization, and deployment; SpikeCredit instead exploits membrane potentials and spike events for sparse-reward credit assignment.The paper describes it, to the authors’ knowledge, as the first spiking RL framework to use these distinct temporal characteristics for that purpose.Source: Spiking RL · pp. 2–3

Preliminaries

Sparse-reward RL provides only a terminal outcome, leaving multiple transition-level credit assignments possible. The spiking actor exposes internal temporal dynamics that can serve as candidate Temporal Credit Carriers.

Sparse-Reward RL

  • With no intermediate rewards, the terminal trajectory outcome can fit multiple transition-level credit assignments.Source: Sparse-Reward RL · p. 3

Spiking Actor

  • The spiking actor encodes each state as a population-coded spike train, processes it with a spiking MLP, and decodes its output into a continuous action.Source: Spiking Actor · p. 3
  • The MLP’s membrane-potential traces and spike events are candidate TCCs, with carrier state selected as membrane-based or spike-based.Source: Spiking Actor · p. 3

Methodology

SpikeCredit treats spiking actor dynamics as task-adaptive Temporal Credit Carriers and couples transition-level credit recovery with updates that make future dynamics more credit-readable.

Methodology

  • SpikeCredit selects task-adaptive Temporal Credit Carriers, reads transition-level credit from current dynamics, and writes recovered targets back to improve future credit readability.The framework closes the loop between post-episode credit reading and replay-based updates to the actor.Source: Methodology · p. 4, Closed-Loop Optimization · p. 5

Task-Adaptive TCC Selection

  • Task-adaptive selection uses a training-free event score: stronger rhythmic or event-oriented structure favors spike-based carriers, while smoother dynamics favor membrane-based carriers.The candidate carriers are membrane traces, which provide graded temporal integration, and spike events, which provide localized event markers.Source: Task-Adaptive TCC Selection · p. 4

Fast Pathway: SMF for TCC Reading

  • Self-Motion Feedback Constraint uses behavior-grounded temporal anchors to constrain inference from TCC dynamics; its proxy is a temporal constraint, not an additional reward signal.Recovered credit is converted into redistributed rewards and targets that indicate above-, at-, or below-uniform credit.Source: Fast Pathway: SMF for TCC Reading · pp. 4–5

Slow Pathway: CTT for TCC Writing

  • Credit-Targeted Trace Alignment matches future TCC scores to SMF-recovered targets, writing episode-level credit into the actor through replay-based updates.The scorer is frozen during actor updates, so the alignment loss updates the actor rather than changing the credit estimator.Source: Slow Pathway: CTT for TCC Writing · p. 5

Closed-Loop Optimization

  • After each episode, the fast pathway recovers credit and redistributed rewards; the slow pathway uses redistributed rewards for critic updates and aligns future TCC dynamics during delayed actor updates.The closed-loop procedure updates twin critics with redistributed rewards and adds CTT to the delayed actor objective.Source: Closed-Loop Optimization · p. 5

Experiment

Across four sparse-reward MuJoCo tasks, SpikeCredit improves on sparse SNN baselines, while analyses examine carrier selection, recovered credit, behavior-grounded cues, and component ablations. The experiments report five-seed results and compare SpikeCredit with dense-reward and alternative credit-assignment methods.

Effective Credit Recovery with SpikeCredit

Experimental Setup

  • The evaluation uses Ant, Hopper, Swimmer, and Walker2d with intermediate rewards zeroed and the undiscounted return revealed only at termination or truncation.Results are reported over five random seeds.Source: Experimental Setup · pp. 5–6

Effective Credit Recovery with SpikeCredit

  • On Swimmer, SpikeCredit exceeds the dense-reward baseline by approximately 113%.On Hopper and Walker2d it approaches dense-reward performance, while a larger gap remains on Ant.Source: Effective Credit Recovery with… · p. 6, Figure 4 · p. 6
  • SpikeCredit achieves the highest average performance on all four tasks versus uniform mean redistribution, rate-coded TCCs, and time-shuffled TCCs.The alternatives remove transition-specific differentiation, fine-grained temporal dynamics, or trajectory alignment, respectively.Source: Effective Credit Recovery with… · p. 6, Figure 4 · p. 6

Mechanistic Analysis

  • Membrane traces perform best on Ant and Hopper, while spike events perform best on Swimmer and Walker2d.The task-event score selects the carrier; stronger event structure favors spikes, while weaker signatures favor graded membrane dynamics.Source: Mechanistic Analysis · pp. 6–7, Figure 5 · p. 7
  • On Ant, SpikeCredit's credit signals correlate with dense rewards at 0.63/0.64 transition-wise and 0.62/0.67 over temporal profiles, while sparse SNN signals are nearly uncorrelated.Dense rewards serve only as a diagnostic reference.Source: Mechanistic Analysis · p. 7, Figure 6 · p. 7
  • SMF relies mainly on state and state-change features, with limited action-energy contribution; its dominant self-motion cues vary by task.The leading cues are forward velocity on Ant, joint and foot velocities on Hopper and Walker2d, and pose and coordinated joint motion on Swimmer.Source: Mechanistic Analysis · p. 7, Figure 7 · p. 7

Ablation Analysis

  • On Ant, removing st, ∆st, or ∥at∥2 2 reduces Last10 return from 1669.9±402.8 to 544.4, 1106.3, or 845.8; removing SMF yields 192.7 ± 78.6.Removing st or SMF limits peak learning to 20K steps, while the full model improves until nearly 1M; removing CTT lowers Last10 from 1669.9 to 1403.8 and peak return from 1777.5 to 1514.5.Source: Ablation Analysis · p. 7, Table 1 · p. 7

Conclusion

SpikeCredit uses spiking dynamics as temporal credit carriers in a closed read-write loop for sparse-reward RL. It outperforms sparse-reward ANN and SNN baselines across four MuJoCo tasks, and its recovered credit captures meaningful temporal structure.

Conclusion

  • SpikeCredit uses spiking dynamics as temporal credit carriers in a closed read-write loop and consistently outperforms sparse-reward ANN and SNN baselines across four MuJoCo tasks.Mechanistic analyses show that the recovered credit captures meaningful temporal structure.Source: Conclusion · p. 7

Dynamic neuron model

The SNN actor uses a second-order Dynamic Neuron with membrane potential and an adaptation variable. Its described update includes synaptic-current decay, spike-triggered state changes, Euler integration, and threshold-based spike generation.

Dynamic neuron model

  • The second-order Dynamic Neuron maintains membrane potential V and adaptation variable U, enabling richer internal dynamics than the standard leaky integrate-and-fire neuron.Source: Dynamic neuron model · p. 10
  • The synaptic current update uses an affine layer input and a decay factor α.Source: Dynamic neuron model · p. 10
  • A spike from the previous step resets membrane potential to θr and increments U by θs before the state is integrated.Source: Dynamic neuron model · p. 10
  • The neuron state is updated using explicit Euler discretization with unit step size, with θv and θu governing adaptation dynamics.Source: Dynamic neuron model · p. 10
  • A spike event is generated using firing threshold Vth and the Heaviside step function.Source: Dynamic neuron model · p. 10
  • During backpropagation, the derivative is approximated with a rectangular surrogate whose window is denoted w.Source: Dynamic neuron model · p. 10

Actor-critic architectures

The compared methods use TD3 with identical twin ANN critics and differ in actor architecture. The SNN actor exposes membrane traces and spike events as candidate temporal credit carriers, while the ANN baseline uses a conventional MLP actor.

Actor-critic architectures

  • All compared methods use TD3 with two identical ANN-based Q-network critics, leaving SpikeCredit's changes on the actor side.Each critic takes concatenated state-action input, uses two 256-unit ReLU hidden layers, and outputs a scalar Q-value.Source: Actor-critic architectures · p. 10
  • The SNN actor population-encodes observations, processes them with a two-layer Dynamic Neuron spiking MLP, and decodes continuous actions; hidden membrane traces and spike events are candidate TCCs.Source: Actor-critic architectures · p. 10
  • The ANN baseline uses a two-layer MLP actor with 256-unit ReLU hidden layers and a tanh output scaled to action bounds, while retaining the same critic and TD3 procedure as SNN baselines.Source: Actor-critic architectures · p. 10

Experiment environments

The experiments use four MuJoCo locomotion tasks with sparse rewards, shared configurations, and semantic observation-feature groupings for attribution. Sensitivity tests show SpikeCredit remains above both baselines across tested hyperparameter values.

Experiment environments

  • Evaluation spans Ant-v4, Hopper-v4, Swimmer-v4, and Walker2d-v4, locomotion tasks with different morphologies and control dynamics, using rewards sparsified from the original dense rewards.The environments are shown in Figure 8.Source: Experiment environments · p. 10, Figure 8 · p. 11

Spiking neuron parameters

  • SNN-based methods share DN parameters and surrogate-gradient configuration across tasks, with neuron-dynamics parameters and the surrogate-gradient window fixed throughout.Table 2 summarizes the dynamic neuron parameters.Source: Spiking neuron parameters · p. 10, Table 2 · p. 12

Actor-critic architecture hyperparameters

  • All methods use the same TD3 framework and twin-critic architecture; hidden-layer configurations are fixed, while actor architecture differs and task dimensions affect input and output sizes.Here, ds and da denote observation and action dimensions, respectively.Source: Actor-critic architecture… · p. 10, Table 3 · p. 12

RL and SpikeCredit hyperparameters

  • Tasks share the training budget, TD3 optimization schedule, and shared SpikeCredit hyperparameters; λCTT and λsparse are task-specific, and BN recalibration applies only to SNN methods.Table 4 summarizes the training, TD3, and SpikeCredit settings.Source: RL and SpikeCredit hyperparameters · p. 10, Table 4 · p. 13

Observation-space categorization

Sensitivity analysis of SpikeCredit

  • Across all tested λalign, λsparse, and λCTT values, SpikeCredit stays above Sparse SNN and Mean Redistribution; moderate alignment and sparsity perform best, while higher λCTT improves return.Overly strong alignment or overly weak sparsity reduces performance but does not collapse learning.Source: Sensitivity analysis of SpikeCredit · p. 11, Figure 9 · p. 14

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