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arxiv: 1906.09781 · v1 · pith:MKOVA43Unew · submitted 2019-06-24 · 💻 cs.LG · stat.ML

In Hindsight: A Smooth Reward for Steady Exploration

Hadi S. Jomaa , Josif Grabocka , Lars Schmidt-Thieme This is my paper

Pith reviewed 2026-05-25 17:36 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords Q-learninghindsight factoroverestimation errorAtari gamestemporal difference learningdeep reinforcement learningadaptive learning rate
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The pith

Adding a hindsight factor that folds past temporal differences into the Q-learning loss reduces overestimation and raises scores on Atari games.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends classical Q-learning by adding a hindsight factor to the loss. This factor folds the historic temporal difference into the reward signal so that updates consider how the model has already progressed, not only expected future returns. In a deterministic continuous-state estimation task the change measurably lowers overestimation and improves stability. On Atari games the resulting agent records higher average scores than deep Q-networks, double deep Q-networks and dueling networks after ten million frames while producing lower action values. The hindsight factor is presented as an adaptive learning rate whose step size depends on the previously estimated action value.

Core claim

The hindsight factor is an additional loss term that integrates the historic temporal difference as part of the reward. When added to the standard temporal-difference objective it reduces overestimation in action-value estimates, yields more stable learning in a deterministic continuous-state function estimation problem, and produces higher average episode scores together with lower action values on a range of Atari games relative to deep Q-network, double deep Q-network and dueling-network baselines after training for ten million frames.

What carries the argument

The hindsight factor, an extra loss term that treats the historic temporal difference as an adaptive learning rate dependent on the previously estimated action value.

If this is right

  • Action-value estimates remain closer to true returns, supporting more reliable deterministic policy evaluation.
  • Average episode reward increases across multiple Atari environments relative to standard Q-learning variants.
  • Training stability improves in continuous-state deterministic settings where overestimation normally grows.
  • The effective learning rate adapts automatically to prior value estimates without external optimizer changes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same historic-difference term could be tested as a drop-in addition to other off-policy algorithms that suffer from overestimation.
  • Because the factor depends only on quantities already computed during training, it may be combined with existing replay buffers at negligible extra cost.
  • If the adaptive-rate interpretation holds, the hindsight term might be re-derived for continuous-action methods where overestimation is also a known issue.

Load-bearing premise

That folding the historic temporal difference into the loss will shrink overestimation without introducing offsetting biases or slowing convergence in the regimes tested.

What would settle it

A controlled run on the same Atari games in which the hindsight-augmented agent shows equal or higher overestimation errors and lower average scores than the plain DQN baseline after identical training.

Figures

Figures reproduced from arXiv: 1906.09781 by Hadi S. Jomaa, Josif Grabocka, Lars Schmidt-Thieme.

Figure 1
Figure 1. Figure 1: Illustration of Overestimations the states. Hence at every frame, we store the transitions (sj , sj+1, aj , Q(sj , aj ; θj ), rj ) in the memory. The goal is to improve the performance of the Q-function, by introduc￾ing updates that do not emphasize solely on the future dis￾counted reward, but also take into account not to deviate from the values associated with decisions in the agent’s experience in older… view at source ↗
Figure 2
Figure 2. Figure 2: Performance curves for various ATARI games using variants of Q-learning techniques; DDQN(dark blue),DDQN [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance curves with δ = 1 and δ = 1 2 ; DQN￾H(cyan), DDQN-H(green), DUEL-H(yellow), DQN-H-HALF(red), DDQN-H-HALF(dark blue), DUEL-H-HALF(pink) Optimizing the Q-function using the hindsight factor as a reg￾ularizer to smoothen the expected reward turns out to improve the performance well before the action-values seem to con￾verge. However, with some games we notice that the perfor￾mance is negatively ef… view at source ↗
Figure 3
Figure 3. Figure 3: Performance curves for ASTERIX where the baselines [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

In classical Q-learning, the objective is to maximize the sum of discounted rewards through iteratively using the Bellman equation as an update, in an attempt to estimate the action value function of the optimal policy. Conventionally, the loss function is defined as the temporal difference between the action value and the expected (discounted) reward, however it focuses solely on the future, leading to overestimation errors. We extend the well-established Q-learning techniques by introducing the hindsight factor, an additional loss term that takes into account how the model progresses, by integrating the historic temporal difference as part of the reward. The effect of this modification is examined in a deterministic continuous-state space function estimation problem, where the overestimation phenomenon is significantly reduced and results in improved stability. The underlying effect of the hindsight factor is modeled as an adaptive learning rate, which unlike existing adaptive optimizers, takes into account the previously estimated action value. The proposed method outperforms variations of Q-learning, with an overall higher average reward and lower action values, which supports the deterministic evaluation, and proves that the hindsight factor contributes to lower overestimation errors. The mean average score of 100 episodes obtained after training for 10 million frames shows that the hindsight factor outperforms deep Q-networks, double deep Q-networks and dueling networks for a variety of ATARI games.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes augmenting standard Q-learning with a 'hindsight factor'—an additive loss term that incorporates the historic temporal difference—to reduce overestimation bias. It evaluates the modification on a deterministic continuous-state function estimation task (claiming reduced overestimation and greater stability) and reports that the resulting agent achieves higher mean average scores than DQN, Double DQN, and Dueling DQN on multiple ATARI games after 10 million training frames.

Significance. If the empirical gains are reproducible and attributable to the hindsight term, the approach supplies a lightweight, interpretable mechanism that adapts the effective learning rate using past value estimates, offering a potential complement to existing overestimation mitigations such as Double Q-learning.

major comments (2)
  1. [Abstract / experimental evaluation] Abstract and experimental results: the manuscript asserts outperformance on ATARI games (mean score over 100 episodes after 10 M frames) and reduced overestimation on the deterministic test problem, yet supplies no implementation details, network architectures, hyper-parameter schedules (including the hindsight coefficient), replay-buffer settings, or statistical tests; without these it is impossible to attribute the reported gains to the hindsight factor rather than other experimental choices.
  2. [Abstract / deterministic evaluation paragraph] The modeling of the hindsight factor as an 'adaptive learning rate' that depends on previously estimated action values is presented as an explanatory device, but the manuscript does not derive or bound the net effect on overestimation bias; it therefore remains unclear whether the additional historic-TD term produces a consistent reduction or merely trades one bias for another under the tested regimes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address each point below and will incorporate the requested clarifications and additions into the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract / experimental evaluation] Abstract and experimental results: the manuscript asserts outperformance on ATARI games (mean score over 100 episodes after 10 M frames) and reduced overestimation on the deterministic test problem, yet supplies no implementation details, network architectures, hyper-parameter schedules (including the hindsight coefficient), replay-buffer settings, or statistical tests; without these it is impossible to attribute the reported gains to the hindsight factor rather than other experimental choices.

    Authors: We agree that the absence of these details prevents full reproducibility and clear attribution of gains. In the revised manuscript we will add: (i) the exact network architectures (CNN for ATARI, MLP for the deterministic task), (ii) all hyper-parameter values and schedules including the hindsight coefficient, (iii) replay-buffer size, sampling strategy and any prioritization, and (iv) statistical reporting (means and standard deviations across multiple random seeds together with significance tests). These additions will allow readers to verify that the reported improvements stem from the hindsight term. revision: yes

  2. Referee: [Abstract / deterministic evaluation paragraph] The modeling of the hindsight factor as an 'adaptive learning rate' that depends on previously estimated action values is presented as an explanatory device, but the manuscript does not derive or bound the net effect on overestimation bias; it therefore remains unclear whether the additional historic-TD term produces a consistent reduction or merely trades one bias for another under the tested regimes.

    Authors: The manuscript introduces the adaptive-learning-rate interpretation only as an intuitive device. We acknowledge that no formal derivation or bias bound is supplied. In revision we will either (a) derive the effect of the historic-TD term on overestimation under the deterministic setting or (b) augment the experimental section with additional controlled experiments that isolate the bias change, thereby clarifying whether the net effect is a consistent reduction. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper introduces the hindsight factor as an explicit new additive loss term that incorporates historic temporal difference into the standard Q-learning objective. This is a definitional extension rather than a re-expression of fitted quantities or a reduction of predictions to inputs by construction. No self-citation load-bearing steps, uniqueness theorems, or ansatzes smuggled via prior work are described; the central mechanism is presented as an independent modification whose effects are then evaluated empirically on deterministic toy problems and ATARI benchmarks. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 1 invented entities

The central claim rests on the introduction of the hindsight factor as a useful additive loss term whose only support is the reported experiments; no independent derivation or external benchmark is supplied.

free parameters (1)
  • hindsight factor coefficient
    A scalar weighting the historic term is required to define the modified loss; its value is not stated in the abstract.
invented entities (1)
  • hindsight factor no independent evidence
    purpose: Additional loss term that folds historic temporal difference into the reward signal
    New component introduced by the paper; no external falsifiable prediction is given.

pith-pipeline@v0.9.0 · 5772 in / 1293 out tokens · 34234 ms · 2026-05-25T17:36:58.239071+00:00 · methodology

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Reference graph

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