Curious Replay in Reinforcement Learning

• Curious Replay is a selective experience replay strategy that prioritizes informative transitions, such as those with high TD errors or novel states, to boost learning efficiency.
• It employs methodologies like prioritized buffers, state recycling, and generative replay to optimize sample selection and mitigate variance in both model-free and model-based approaches.
• Its applications extend to reinforcement learning, continual learning, distributed computing, and neuroscience, demonstrating significant theoretical and empirical impact.

Curious Replay refers to a spectrum of experience replay strategies in reinforcement learning and related fields that emphasize the selective reuse or generation of transitions, episodes, or state–action pairs that are considered “informative,” “surprising,” or intrinsically “novel,” as opposed to uniform or randomly chosen samples. The central idea is to focus computational resources on experiences that are expected to induce the highest learning progress, typically by leveraging criteria such as temporal-difference (TD) error, model prediction uncertainty, intrinsic motivation/curiosity signals, or explicit measures of behavioral novelty. Mechanisms have been extensively developed for both model-free and model-based RL, with methodological innovations ranging from prioritized buffers, state recycling, curiosity-driven diffusion generative models, resampling theory for variance reduction, to the replay and visualization of compositional event structures in distributed systems.

1. Fundamentals of Curious Replay

Curious replay emerged initially as an extension of standard experience replay, motivated by the observation that only a minority of past transitions (e.g., those with high TD error, rare events, or in poorly understood regions) are critical for accelerating an agent’s learning. In classic experience replay, transitions are stored in a buffer and sampled uniformly (Schaul et al., 2015). However, prioritized experience replay (PER) assigns each transition a priority, often $|δ|$ (TD error magnitude), so that transitions that have elicited larger temporal-difference errors—interpretable as “surprising” or “curious”—are more likely to be sampled:

$P(i) = \frac{p_i^\alpha}{\sum_k p_k^\alpha}$

Here, $p_i$ (priority) often takes the form $|δ_i| + ε$, with $α$ controlling prioritization level. PER also integrates importance sampling to correct for distributional shift:

$w_i = \left(\frac{1}{N \cdot P(i)}\right)^\beta$

normalized by $\max_i w_i = 1$.

Such mechanisms represent the foundational “curious replay” paradigm—sampling is explicitly biased toward transitions the agent has not yet mastered. Extensions also explore the idea of reusing entire sequences rather than single transitions, especially when high TD errors propagate non-locally (Karimpanal et al., 2017).

2. Advanced Prioritization: Model-based and Double Prioritized Replay

Curious replay strategies have branched into more nuanced prioritization schemes. For example, Double Prioritized State Recycled Experience Replay (DPSR) augments the classic PER formulation with prioritization both at sampling and buffer replacement (Bu et al., 2020). When inserting new experiences, candidates for replacement are sampled with probability inversely proportional to their priority:

$PR_i = \frac{p_i^{-γ(t)}}{\sum_j p_j^{-γ(t)}}$

where $γ(t)$ tunes the influence of priority over time.

DPSR introduces a state recycling mechanism: before discarding a low-priority transition, its starting state is re-fed to the Q-network, and an alternative action is executed to generate a potentially more informative transition. The highest-scoring recycled experience replaces the original, mitigating premature loss of low-priority (but possibly later useful) data.

These schemes support empirical gains: for example, DPSR achieved a median 87–92% improvement over uniform replay and classic PER across 24 Atari games (Bu et al., 2020).

3. Generative and Model-driven Curious Replay

Recent work generalizes curious replay to parametric memory systems using conditional generative diffusion models (Wang et al., 23 Oct 2024). In Prioritized Generative Replay (PGR), a conditional diffusion model $G$ is trained to densify agent experience by sampling synthetic transitions:

$\tau = (s, a, s', r)$

conditioned on a relevance function $\mathcal{A}(\tau)$ drawn from several families:

• Return-based: $\mathcal{A}(s, a, s', r) = Q(s, π(s))$
• TD error-based: $$\mathcal{A}(s, a, s', r) = r + γ Q_{target}(s', \arg\max_{a'} Q(s', a')) - Q(s, a)$$
• Curiosity-based: $$\mathcal{A}(s, a, s', r) = \frac{1}{2} \|g(h(s), a) - h(s')\|^2$$ (where $h$ is a learned encoder, $g$ a forward model)

The conditional generator can focus on underexplored or high-novelty regions—advancing beyond overfitting-prone value-based densification—by using CFG (classifier-free guidance) during sampling.

Empirically, curiosity-conditioned PGR increases both diversity of replayed transitions and sample efficiency, yielding higher performance and allowing very high update-to-data (UTD) ratios—i.e., performing many gradient steps per environment sample without performance collapse.

4. Intrinsic Motivation, Hindsight, and Model Uncertainty

Curious replay is often tightly coupled to mechanisms of intrinsic motivation. Agents compute curiosity as prediction error of a learned world model, e.g.:

$$r^i = \nu \cdot \operatorname{StdDev}[f_{ensemble}^{next}(s, a)] \quad \text{(ensemble disagreement)}$$

or

$r^i = \|f_{pred}(s, a) - s'\|^2$

This error, reflecting epistemic uncertainty, guides both exploration and replay prioritization. Combined with Hindsight Experience Replay (HER), such mechanisms enable agents to learn in sparse-reward, multi-goal environments (Lanier et al., 2019, McCarthy et al., 2021), and further boost sample efficiency by generating and relabeling failed transitions with achievable goals, augmented by intrinsic motivation (Li et al., 2020).

Curriculum learning is integrated in curiosity-driven HER systems to scaffold the learning of complex tasks (e.g., multi-block stacking), ensuring that the agent is exposed to increasingly complex and informative experiences (Lanier et al., 2019).

5. Variance Reduction and Theoretical Guarantees

A rigorous statistical underpinning for curious replay emerges when replay-based estimators are analyzed as resampled U- and V-statistics. Experience replay updates can be rewritten as averages over randomly drawn batches:

$\frac{1}{B} \sum_{i=1}^B h_k(b_i)$

where each $h_k$ is a batch-based update kernel.

Resampling leads to asymptotic normality:

$$\sqrt{n}(\tilde{\theta}_n - \theta) \xrightarrow{d} N(0, \Sigma)$$

and strictly lower variance compared to single-pass “plug-in” estimators, with variance formulas detailed via the covariance components $\zeta_{c,k}$ (Han et al., 1 Feb 2025).

This framework not only provides theoretical guarantees of variance reduction in policy evaluation (e.g., LSTD, PDE-based algorithms) but also enables computational savings, e.g., reducing kernel ridge regression from $O(n^3)$ to $O(n^2)$.

6. Sampling Regimes: Reshuffling, Overfitting, and Replay Effects

Uniform sampling with replacement permits high variance; integrating random reshuffling (RR) ensures that every sample in the buffer is used exactly once per epoch—translating to lower variance and improved convergence rates (e.g., $O(1/K^2)$ for smooth/strongly convex problems) (Fujita, 4 Mar 2025). RR can be extended to prioritized buffers by tracking expected versus actual sampling counts and “masking” transitions that are oversampled.

Conversely, recent theoretical work demonstrates that, in continual learning, naive replay can increase forgetting if subspace alignments between tasks are unfavorable or if the replay ratio is suboptimal. Forgetting can exhibit non-monotonic dependence on the number and type of replayed samples, sometimes worsening as replay increases up to a threshold (Mahdaviyeh et al., 4 Jun 2025).

The evolution of parameter error in linear regression continual learning can be formalized as:

$w_t - w^* = P_t (w_{t-1} - w^*)$

where $P_t$ is the projection into the null space of the $t$-th task.

Empirical studies also expose analogous effects in nonlinear networks and deep RL agents, emphasizing the need for careful adaptive replay strategies.

7. Broader Domains and Systems: Distributed Algorithms and Biological Perspectives

Curious replay generalizes further beyond RL. In distributed computing, replay clocks (RepCl) introduce a timestamping infrastructure enabling the offline exploration of alternative interleavings of concurrent events—termed “curious replay”—supporting rigorous debugging and process visualization (Lagwankar, 18 Jun 2024). Replay clocks construct event orderings that respect causality but avoid imposing artificial serial order on truly concurrent actions.

In neuroscience, replay in the hippocampus has been proposed as a substrate for compositional computation—binding entities to structural “roles” and sequencing them to form novel knowledge not present in direct experience (Kurth-Nelson et al., 2022). This conception of replay as a combinatorial synthesizer connects to the broader theme of curiosity-driven recombination in both artificial and biological intelligence.

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Curious Replay thus encapsulates a class of adaptive, priority-driven experience selection and generation mechanisms that have deep theoretical, algorithmic, and empirical impact across reinforcement learning, continual learning, variance reduction, generative modeling, distributed computation, and biological memory systems. Its central principle is: the learning system should focus on experiences that are both “curious”—highly informative, novel, or surprising—and relevant for inducing progress on the underlying task.