{"id":"a4a25bdf-c530-49c6-8084-72853e1d942c","arxiv_id":"2412.00044","paper_version":1,"verdict":"REJECT","confidence":"LOW","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A hand-designed nested reward formula with a secondary multi-output network is claimed to improve PPO on Pendulum-v1, but the method is underspecified and the evidence is anecdotal.","lead":"This paper proposes adding a second neural network that outputs several reward signals, combined by a hand-written formula, to help a reinforcement learning agent learn faster. The authors report better scores on a pendulum balancing task, but the method is not fully specified and the results have no error bars.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No training objective or update rule is given for the reward agent; without it, the hierarchical mechanism in Section IV-B is unspecified, so the Pendulum-v1 gains in Section V-A cannot support the paper's central claim.","rationale":"The reader's weakest assumption is exactly the load-bearing concern: the reward agent has no stated training objective or update rule. The central claim is not just an empirical claim about Pendulum-v1; it is a mechanistic claim that a hierarchy of needs emerges from the rewarding agent's scalar outputs. Without a training signal for r1, r2, r3, the architecture alone cannot produce that mechanism. The empirical results in Section V-A are also anecdotal, but even taking them at face value, they cannot be attributed to the proposed hierarchical mechanism unless the reward agent is actually learned. The concrete test of freezing the reward agent would settle whether the reported gains depend on learning: if they do not, the paper's mechanism is not what causes the improvement; if they do, the paper still needs to specify the training objective before the method is reproducible. The paper's own acknowledgement that the linear model is simplistic supports the view that the derivation is incomplete. I would keep the reader's REJECT verdict because the method is under-specified and the central claim is therefore unsupported as written.","tokens_in":4761,"tokens_out":4905,"duration_ms":45885,"concrete_test":"Run the Pendulum-v1 experiment with the reward agent's weights frozen at initialization, using the same five seeds and 100-episode evaluation as described in Section V-A. If the frozen version reproduces the reported advantage or the -125 TLA score, the result does not depend on a learned hierarchy; if it degrades, the missing update rule for r1, r2, r3 must be disclosed and specified before the claim can be assessed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing condition for the central claim is that the reward agent's three outputs r1, r2, r3 are learned signals that encode a hierarchy of needs. The paper never states how those outputs are trained. Section IV-B specifies only the architecture (5 layers, 64 units, 3 linear output neurons) and gives the nested formula r = R(r1(r2r3 + r2) + r1) + R, called a rewrite of Section III's r = Rr1 + R. No loss function, optimizer, gradient path, or reward-agent update rule appears anywhere. If r1, r2, r3 are initialized and frozen, the final reward is just a fixed nonlinear transformation of the environment reward R and random state features; no hierarchy can emerge, and the claimed improvements in Section V-A (faster learning, stability, and -125 versus -154 against TLA) would be unexplained or misattributed. The paper's own Future Work section admits that the linear model 'may not accurately capture the complexities of real-world systems,' reinforcing that the equation is asserted rather than derived. The central claim therefore rests on an unspecified component.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a 'secondary rewarding agent' whose multiple scalar outputs are combined with the global reward by the equation r = R(r1(r2r3 + r2) + r1) + R, claimed to induce a hierarchical disposition of needs in a PPO agent. The authors report faster learning, greater stability, and higher rewards than PPO on Pendulum-v1, and a single comparison score of -125 against -154 for the TLA algorithm, described as state of the art. The manuscript also sketches a future graph-based reward model. The contribution is presented as a conceptual mechanism plus preliminary experiments.","tokens_in":5026,"tokens_out":2321,"duration_ms":21626,"significance":"If the hierarchical-reward mechanism were sound and the empirical claims reproducible, the paper would address a relevant question in reward shaping and hierarchical RL. The main strength is that the proposal is concrete and makes a falsifiable prediction, and the discussion honestly acknowledges the limitations of the linear reward model in Section VI. However, the conceptual claim is currently asserted rather than derived, the key training objective for the reward agent is missing, and the experimental evidence consists of one learning curve and one unpaired score with no error bars. The significance of the paper is therefore not yet established.","major_comments":[{"comment":"The training objective for the reward agent is never specified. Section IV-B gives only the architecture (5 layers, 64 units, 3 linear output neurons) and the nested formula r = R(r1(r2r3 + r2) + r1) + R, but no loss function, optimizer, update rule, or gradient path for r1, r2, r3. Since the final reward is a fixed nonlinear function of R and the reward-agent outputs, if those outputs are initialized and frozen, the proposed hierarchy cannot emerge. The learning gains attributed to the hierarchy in Section V-A are therefore unexplained unless the reward agent is trained, and the paper does not state how.","section":"Section III"},{"comment":"The 'derivation' of r = Rr1 + R is not a derivation; it is an ansatz. The claim that this equation sets up a two-stage hierarchy by correlating r1 and R is a restatement of the equation's structure, not an independent derivation of hierarchy. Moreover, the sentence 'All the while training the critic solely with the global reward R' conflicts with the abstract's claim that the traditional agent learns to maximize the scalar outputs in a hierarchical manner. The paper must state clearly which network is trained with which objective.","section":"Section IV"},{"comment":"The experimental evidence is insufficient to support the central claim. The reported 'FIG 2' is not included in the manuscript, so the faster-learning and stability claims have no visible supporting data. The state-of-the-art claim rests on a single score from 'another run' (-125 vs -154), without error bars, number of seeds, hyperparameter settings, or a description of the TLA baseline. Additionally, Section IV-A conflates Pendulum-v0 and Pendulum-v1, and the five-seed evaluation protocol stated in Section IV is not reflected in the reported results. Reproducibility and statistical support are both lacking.","section":"Section IV-A"},{"comment":"The paper's own future-work section states that the linear model 'may not accurately capture the complexities of real-world systems.' This admission reinforces that the central equation is an unvalidated assumption rather than a derived result. If the authors intend to claim that the equation induces a hierarchy of needs, they need to provide a formal argument or at least an ablation study isolating the contribution of the hierarchical structure from the extra parameters of the reward agent.","section":"Section VI"}],"minor_comments":[{"comment":"There are several typographical errors: 'heirarchy' should be 'hierarchy', 'soley' should be 'solely', and 'sclaar' appears in the text; the manuscript should be proofread.","section":"Global"},{"comment":"The environment is named Pendulum-v1 in the heading but Pendulum-v0 in the text; please correct the inconsistency.","section":"Section IV-A"},{"comment":"The reference to 'FIG 2' does not correspond to any figure in the manuscript; either include the figure or remove the reference.","section":"Section V-A"},{"comment":"Reference [19] is formatted differently from the others and should be completed with the publication venue and year.","section":"References"}],"recommendation":"reject","confidential_remarks":"The manuscript reads like an extended abstract rather than a complete research paper. The missing training objective for the reward agent is not a minor omission; it is the mechanism that would make the hierarchy claim meaningful. Adding it would require substantial new content, as would the proper experiments. I do not see a path to acceptance without essentially rewriting the core sections."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Thanks for the pointer. The short version: there's a real idea in here — using a secondary network with multiple scalar outputs to reshape rewards in a nested way — but the paper never specifies how that network is trained, so the experimental gains can't be attributed to the proposed mechanism. That's not a fixable typo; it's the load-bearing component.\n\nWhat's new is the specific nested reward equation r = R(r1(r2r3 + r2) + r1) + R applied to PPO and TLA on Pendulum-v1. I haven't seen that exact combination in the citations. The paper is also honest in the Future Work section that the linear model is simplistic and a graph-based version is needed. That self-assessment is accurate.\n\nThe soft spots are serious. The reward agent's training objective is never stated. Section IV-B gives the architecture (5x64 tanh, 3 linear outputs) but no loss function or update rule. If those outputs are random or frozen, the final reward is just a fixed nonlinear transform of R, and no hierarchy emerges. The hierarchy claim in Section III is circular: the equation is asserted to induce prioritization, but no derivation links the arithmetic to nested optimization. The experiments are one environment, no error bars, one learning curve, and the 'state of the art' comparison is a single run (-125 vs -154) against TLA from a separate run. The paper says five seeds were trained but the results section doesn't report variance. There's also an inconsistency: Section IV-A says Pendulum-v0 while the abstract and elsewhere say v1.\n\nSo the central claim — that this reward structure improves learning via a hierarchical disposition — is unsupported. The empirical result may be real, but with no mechanism specified and no statistical grounding, it's an anecdote. The citation pattern is also thin: standard RL papers, but no reward shaping or hierarchical RL literature, despite the claim being squarely in that area.\n\nFor peer review: this is a desk reject for any serious venue. It's a workshop-level sketch. If the author adds the reward-agent training objective, ablations (random vs learned r1, r2, r3), and error bars over seeds on at least one more environment, it could become a publishable short paper. As is, I wouldn't send it to referees.","headline":"A reward-shaping sketch with a plausible intuition but no specified training mechanism for the reward agent, so the Pendulum-v1 gains are not attributable to the claimed hierarchy.","tokens_in":5450,"tokens_out":2611,"would_cite":false,"duration_ms":23162,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Nested reward signals produce faster, higher-scoring reinforcement learning on Pendulum-v1.","keywords":["hierarchical reward","hierarchy of needs","reward shaping","proximal policy optimization","continuous control","Pendulum-v1","multi-objective reinforcement learning","reward agent"],"falsifier":"Train the same PPO setup but replace the reward agent's outputs with random or fixed constants; if performance still reaches -125, the hierarchy is not the cause.","tokens_in":4608,"feed_emoji":"🎯","tokens_out":3261,"duration_ms":25273,"temperature":0.7,"pith_summary":"The paper proposes that a second 'rewarding agent' with multiple scalar outputs can impose a hierarchy of needs on a reinforcement learning agent. The main agent is trained with a nested reward equation that forces it to satisfy lower-level rewards before higher-level ones. The authors claim this leads to faster, more stable learning and better final rewards on a standard pendulum control benchmark, outperforming the baseline PPO and, in one run, matching state of the art. The central insight is that simple base rewards can generate complex goal hierarchies, but the mechanism depends on the reward agent producing meaningful signals, which the paper does not specify how to train.","feed_headline":"Hierarchical rewards lift Pendulum-v1 score to -125","feed_subtitle":"A secondary reward network with three priority levels claims faster, more stable PPO learning on a standard benchmark.","key_machinery":"The central mechanism is the nested reward equation combined with a secondary 'reward agent' network that outputs three scalar values. The equation orders the scalar reward components and the global reward by priority, so the main agent's policy gradient is pushed to satisfy lower levels first. The reward agent receives the same state inputs as the main agent and its outputs are meant to be learned signals, but the paper does not state any loss function or update rule for this network.","core_discovery":"The paper claims that introducing a secondary reward network with three scalar outputs, combined by the nested equation $r = R(r_1(r_2r_3 + r_2) + r_1) + R$, induces a hierarchy of needs in the main agent. By conditioning each reward level on the maximization of the previous level, the agent learns to prioritize lower-level needs before higher-level ones, leading to improved global reward. In experiments on Pendulum-v1, the method reportedly learns faster, with greater stability and higher rewards than PPO without these adjustments, and in one run achieves -125 versus -154 for the previous state-of-the-art TLA model.","pith_inferences":["The lack of a training objective for the reward agent is a serious gap; if the reward outputs are fixed or random, the hierarchy may be an artifact of reward scaling rather than a learned structure, and a direct test would be to freeze the reward agent at initialization.","The nested equation may simply act as a static reward-shaping term that reshapes the optimization landscape; comparing against a shaped reward with the same functional form but fixed coefficients would isolate the effect of the learnable reward agent.","The 'state of the art' claim relies on a single run against one baseline; the paper does not report seed variance for the TLA comparison, so the -125 versus -154 gap may not be robust."],"forward_implications":["If this holds, reinforcement learning practitioners could specify simple base rewards and let a reward network grow a hierarchy of goals automatically.","The method adds no extra environment interaction compared to PPO, only an additional network, so it could be dropped into existing PPO codebases without changing the rollout procedure.","The claimed stability gains suggest reduced variance across random seeds, potentially easing hyperparameter tuning and making training more reliable.","The nested equation generalizes to any number of levels, allowing deeper need hierarchies that might tackle more complex objectives."],"supporting_citations":[{"why":"Supplies the PPO algorithm that the baseline and the proposed method extend.","marker":"[5]"},{"why":"Provides generalized advantage estimation used in the policy update.","marker":"[10]"},{"why":"Defines the Pendulum-v1 environment used for evaluation.","marker":"[12]"},{"why":"The publicly available PPO implementation that was adapted to include the reward function.","marker":"[13]"},{"why":"The temporally-layered architecture model whose Pendulum-v1 score is the state-of-the-art baseline being compared against.","marker":"[19]"}],"fun_headline_variants":["Hierarchy of needs boosts Pendulum-v1 to -125","Nested reward hierarchy hits -125 on Pendulum-v1","Secondary reward agent prioritizes needs, beats baseline","Reward hierarchy outruns TLA on Pendulum-v1"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the reward agent's three scalar outputs carry meaningful learned signals that create a hierarchy, but the paper never specifies how the reward agent is trained or what objective drives it.","fun_headline_variants_meta":{"raw":{"variants":["Hierarchy of needs boosts Pendulum-v1 to -125","Nested reward hierarchy hits -125 on Pendulum-v1","Secondary reward agent prioritizes needs, beats baseline","Reward hierarchy outruns TLA on Pendulum-v1"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000252,"raw_usage":{"total_tokens":1471,"prompt_tokens":763,"completion_tokens":708,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":379,"completion_tokens_details":{"reasoning_tokens":639}},"tokens_in":379,"tokens_out":708,"duration_ms":5940,"temperature":1.0,"reasoning_tokens":639,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:15:02.939840+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the same PPO setup but replace the reward agent's outputs with random or fixed constants; if performance still reaches -125, the hierarchy is not the cause.","supporting_citations":[{"cited_title":"Pytorch implementations of reinforcement learning algo- rithms,","cited_arxiv_id":null,"evidence_quote":"The publicly available PPO implementation that was adapted to include the reward function."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The temporally-layered architecture model whose Pendulum-v1 score is the state-of-the-art baseline being compared against."}],"review_version":1}