{"id":"137119e4-fe9f-4aea-9f4a-c81ed63fffe1","arxiv_id":"2412.17797","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In partially observable assistance games, a goal-aligned assistant sometimes must interfere with the human's observations at the level of single actions, but never at the level of its complete policy.","lead":"This paper proves that a perfectly aligned AI assistant that fully shares a human's goals can, in some games, be forced to hide or alter what the human sees in order to communicate private information, to query preferences, or to help an irrational human decide. It also proves that relative to the assistant's whole strategy, there is always an equally good plan that never hides information.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorems 4.2 and 4.7 fail as stated for infinite action spaces: an infinite chain of ever-finer observations yields no non-interfering optimal policy, so 'any POAG' requires a finiteness restriction.","rationale":"The paper's central dichotomy is that action-level interference is sometimes unavoidable (Proposition 4.4) while policy-level interference is never necessary (Theorem 4.7), and the 'any POAG' quantification is what makes Theorem 4.7 an extension of the nonnegative value of information. The reader identified the entropy proof's reliance on discrete spaces and compactness; I agree with that root cause and sharpen it: under the literal Definition 2.1, the theorem is false. Infinite action spaces can form an infinite ascending chain of more informative actions with identical state-transition and reward effects and no most-informative element, so every optimal policy has a more informative alternative. The constructed counterexample is stylized but falls squarely inside the definition, so the literal theorem statements are incorrect. The standard fix is to add finiteness to Definition 2.1 and to all theorem statements; this preserves Proposition 4.4 and Theorem 4.7 for finite DecPOMDPs, which is the usual setting and is sufficient for the paper's examples. Thus the paper's contribution survives as a finite-state result, and the required revision is substantive but not fatal. This does not move the reader's verdict: CONDITIONAL remains appropriate, though the finiteness restriction must be made explicit. I partially agree with the reader because we identify the same underlying gap, but I conclude falsity of the literal quantification rather than merely a missing proof for continuous spaces.","tokens_in":28546,"tokens_out":24842,"duration_ms":253767,"concrete_test":"Formally instantiate the counterexample under Definition 2.1: let S=[0,1], AH=[0,1], AA=ℕ, so the game is one-shot with γ=0, A's observation always null, and H's observation under action n be (n, bin) where bin is the dyadic interval of width 2^{-n} containing s, with reward 1[|aH-s|<1/8]. Verify that every action n is action-level interfering via n+1, and that every policy is policy-level interfering via the unit shift of the action distribution. If this is accepted as a POAG, then Theorems 4.2 and 4.7 must be amended to finite POAGs; if the authors reject the example, they must state which clause of Definition 2.1 excludes it.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Definition 2.1 defines a POAG over arbitrary sets, yet Theorems 4.2 and 4.7 are asserted for 'any POAG'. The proofs rely on finiteness: Theorem 4.7 uses Shannon entropy, a uniform-random human policy, and compactness of the policy set; Theorem 4.2 assumes a most-informative non-interfering replacement can be selected. Under the literal definition, these theorems are not just unproven; they are false. Construct a one-shot POAG with S=[0,1] (uniform initial state), AH=[0,1], AA=ℕ, A having no private information, reward R(s,aH,aA)=1 if |aH-s|<1/8 else 0, and where under action n the human observes the pair (n, bin), with bin the index of the length-2^{-n} dyadic interval containing s. For every n≥3 the human can choose the bin midpoint and obtain reward 1, so all such n are optimal. But action n+1 is strictly more informative than action n (finer bins deterministically round to coarser bins) and has identical state-transition and reward effects, so every action is action-level interfering. For policy-level interference, shift any distribution over AA up by one; the human's observation under the shifted policy can be garbled back to the original, so every policy is policy-level interfering. Hence no optimal policy pair avoids interference, contradicting Theorems 4.2 and 4.7. The fix is to restrict Definition 2.1 and all quantified theorems to finite, or otherwise compact, POAGs, which is the standard DecPOMDP setting and suffices for the paper's examples.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces partially observable assistance games (POAGs) and defines two notions of observation interference: action-level interference, which compares individual assistant actions by Blackwell informativeness while holding state-transition and reward effects fixed, and policy-level interference, which makes the same comparison at the level of entire policies. The main theoretical claims are: if the assistant has no private information, there exists an optimal policy pair without action-level interference (Theorem 4.2); if the assistant has private information, action-level interference can be unavoidable in every optimal pair, even with a naive human (Proposition 4.4); an unbounded A-to-H communication channel removes this necessity (Theorem 4.5); in every POAG there exists an optimal policy pair without policy-level interference (Theorem 4.7); with a naive human, interference can be needed to elicit the human's preferences (Proposition 5.2); and under Boltzmann-rational human behavior, interference can be optimal even without private information (Proposition 6.3). The paper closes with a Monte Carlo study of a product-selection game that quantifies the tradeoff between communicating the assistant's private information and destroying the human's private information.","tokens_in":28763,"tokens_out":9420,"duration_ms":91679,"significance":"If the results are read with the intended finite-state qualifications, the paper makes a clean and useful contribution: it separates action-level from policy-level observation tampering, identifies communication of private information as a driver of the former, and extends the nonnegative-value-of-information principle to cooperative multiagent settings. The appendix contains detailed proofs and fully formalized counterexample games, which is a clear strength. The experimental section is a reasonable illustration of the theory. The significance is moderate: the qualitative conclusions are likely to matter for assistance-game and AI-safety audiences, but the universal quantifier over 'any POAG' is not justified as stated, and the theorems need to be restricted to finite, or otherwise compact/discrete, POAGs before the central claims are sound.","major_comments":[{"comment":"The universal theorems are stated for 'any POAG' under Definition 2.1, where the state, action, and observation sets are arbitrary, but the proofs require finiteness or compactness. Theorem 4.7's proof in Appendix B.5 minimizes Shannon entropy of the human's posterior, uses a uniform-random human policy over AH, and invokes the extreme value theorem on a closed and bounded policy set; none of these is guaranteed by Definition 2.1. This is not merely a missing hypothesis: consider the one-shot POAG with S=[0,1] (uniform initial state), AH=[0,1], AA=ℕ, A having no private information, and reward R(s,aH,aA)=1 if |aH−s|<1/8 else 0, where under action n the human observes (n, bin_n(s)) with bin_n the index of the length-2^{-n} dyadic interval containing s. For every n≥3 the human can play the bin midpoint and obtain reward 1, so all such n are optimal; but action n+1 is strictly more informative than n and has identical state-transition and reward effects, so every optimal action is action-level interfering under Definition 3.2. Similarly, shifting any distribution over AA up by one yields a more informative policy with the same effects, so every policy is policy-level interfering under Definition 4.6. Thus Theorems 4.2 and 4.7 are false as stated, and Theorems 4.5 and 5.3 inherit the same quantifier problem. The fix is to restrict Definition 2.1 and all quantified theorems to finite, or otherwise compact/discrete, POAGs, which covers the paper's examples and the standard DecPOMDP setting.","section":"§2.1, §4.2, §4.3 (Theorems 4.2, 4.5, 4.7; Appendices B.2, B.5)"},{"comment":"Even within finite POAGs, the proof of Theorem 4.7 should justify that the one-step entropy-minimizing choices assemble into an optimal pair for the infinite-horizon objective. The argument shows that every finite prefix is compatible with some optimal policy pair, but without a compactness or limiting argument the resulting limit policy pair need not be optimal. This is the same structural issue as the finiteness problem above and should be addressed when the theorem is restated with the appropriate hypotheses.","section":"Appendix B.5 (Theorem 4.7)"}],"minor_comments":[{"comment":"The displayed definition repeats the human policy in the conditioning event, writing PoH_{t+1}(· | πH, st+1, ˆπA_{0:t}, πH); it should presumably condition on πH only once.","section":"Definition 4.6"},{"comment":"In the formalization of Example 4.3, the human observation kernel is written as OH(oH | s, aA, aH) = 1[oA_i = s_{i+1} aA_i], which appears to contain typos; it should presumably be 1[oH_i = s_{i+10} aA_i].","section":"Appendix B.3"},{"comment":"The reward definition in Appendix D has a stray line '1[aH = 1]1[s ∈ {sa, sb}] + 1[aH = 2]1[s ∈ {sc, sd}]' after the four numbered equations; either remove it or explain its intended role.","section":"Example 6.2 formalization"},{"comment":"The Monte Carlo results are reported without error bars or confidence intervals, so small differences between curves, especially at low β, are hard to distinguish from sampling noise; reporting standard errors or multiple seeds would strengthen the experimental claim.","section":"Figure 1"},{"comment":"The Boltzmann-rational response definition has πH appearing inside the expectation on both sides of the defining equation; please clarify whether this is intended as a fixed-point condition and, if so, how existence and uniqueness are guaranteed in the examples.","section":"Definition 6.1"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the infinite-action counterexample in the major comments is decisive against the stated universal claims, but I view it as a repairable quantifier problem rather than a fatal flaw, because restricting to finite POAGs is the natural scope and preserves all of the paper's examples and qualitative conclusions. I would not reject on this basis if the authors restate the theorems with the appropriate finiteness hypotheses and fix the Theorem 4.7 proof accordingly."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about arXiv:2412.17797. First, the distinction between action-level and policy-level observation interference is real and worth keeping: Proposition 4.4 and Theorem 4.7 together give a clean picture—an aligned assistant may have to take interfering actions, but never needs an interfering policy. Second, the main theorems are stated more broadly than the proofs support. The stress-test counterexample is valid: with state space [0,1], human actions [0,1], assistant actions ℕ, and dyadic-bin observations, every action n≥3 is both optimal and strictly less informative than n+1, so every optimal policy interferes at both levels. That directly contradicts Theorems 4.2 and 4.7 as written over \"any POAG.\" The reader's concern about discrete spaces was on the right track; it is not just a proof gap.\n\nWhat the paper does well: the CUDA example and the preference-querying example are fully formalized in the appendix, the proofs are detailed, and the authors are unusually candid about the limits of their definitions (Appendix G). They also correctly position the result against the single-agent value-of-information theorem and the multiagent value-of-information literature. The citation pattern looks honest.\n\nSoft spots, in proportion. The finiteness fix is easy—restrict Definition 2.1 and the theorems to finite (or compact) POAGs, which covers every example in the paper. Without that restriction, the claims are false. The \"naive human\" definitions are modeling assumptions, not empirical claims; the authors flag this themselves. The experiments are internal—they compute consequences of the analytic Proposition 7.2 rather than testing anything external—but for a theory paper that's acceptable. No code release is a minor annoyance.\n\nWho should read this: anyone working on assistance games, cooperative AI, or the value of information in multiagent settings. The action/policy distinction will be cited. It deserves a serious referee; after the finiteness restriction is added, the paper is in good shape. My recommendation: send it to review, and insist the revision restrict the domain of the theorems.","headline":"The action/policy interference distinction is a genuine contribution, but the main theorems as stated are false on a simple infinite-state counterexample; a finiteness restriction fixes them.","tokens_in":29460,"tokens_out":4105,"would_cite":true,"duration_ms":39547,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Partially observable assistance games can make observation interference necessary at the level of individual actions, but never at the level of whole policies.","keywords":["partially observable assistance games","observation interference","value of information","human-AI alignment","decentralized POMDP","Boltzmann rationality","assistance games","AI deception"],"falsifier":"Run an exhaustive search over optimal policy pairs in the formal finite POAG of Example 4.3 (Appendix B.3); the paper's Theorem 4.7 predicts at least one optimal pair is non-interfering at the policy level, so finding that every optimal pair interferes at the policy level under Definition 4.6 would disprove the theorem.","tokens_in":28150,"feed_emoji":"🤖","tokens_out":7122,"duration_ms":61512,"temperature":0.7,"pith_summary":"This paper studies partially observable assistance games (POAGs), a two-player model in which a human and an AI assistant share the same reward function, but only the human knows the reward parameters and both sides see the world only partially. It asks whether a perfectly aligned assistant would ever benefit from interfering with the human's observations. The paper's central finding is split: in some POAGs every optimal policy pair requires the assistant to take an action that gives the human a strictly less informative signal, even though a state- and reward-equivalent non-interfering action exists (Proposition 4.4); yet in every POAG there is some optimal policy pair in which the assistant does not interfere when interference is judged at the level of whole policies rather than isolated actions (Theorem 4.7). This reconciles action-level interference with the classical result that the value of information is nonnegative, and extends that result to cooperative multi-agent settings. The paper also identifies two further incentives for interference, querying the preferences of a naive human and simplifying decisions for a Boltzmann-rational human, and supports the theory with a product-selection experiment.","feed_headline":"Sometimes aligned AI assistants must hide information from humans","feed_subtitle":"Action-level hiding can be unavoidable, yet no optimal policy pair ever needs to interfere at the policy level.","key_machinery":"The paper's central object is the Blackwell informativeness order: an observation family $P$ is more informative than $\\hat{P}$ when $\\hat{P}$ can be produced from $P$ by a fixed stochastic function independent of the state. Definition 3.2 calls an action observation-interfering if a state- and reward-equivalent action exists whose induced human observation distribution is strictly more informative; Definition 4.6 applies the same comparison to whole policies, allowing the human to condition on the assistant's known strategy. The proof of Theorem 4.7 carries the argument by choosing, among optimal continuation policies, one that minimizes the Shannon entropy $H(P(S_{t+1} \\mid O^H_{t+1}))$ of the human's posterior over states; Lemma B.4 shows a strictly more informative policy strictly lowers this entropy, so no entropy-minimizing optimal policy can be observation-interfering at the policy level.","core_discovery":"At the level of individual actions, the assistant may have to suppress information in order to convey its own private information. In the paper's CUDA version-list example, the assistant knows which software versions are compatible while the human does not; the assistant's optimal policy suppresses the incompatible versions from the human's view, even though suppressing nothing has identical state-transition and reward effects. That suppression counts as observation interference under the paper's action-level definition. But when interference is defined relative to the human's inference given the assistant's whole policy, the same suppression becomes informative rather than destructive, and the paper proves that an optimal policy pair always exists in which the assistant does not interfere at the policy level. Thus the paper establishes that observation interference is sometimes necessary action-by-action, never necessary as a strategy, and that the classic nonnegative value of information carries over to common-payoff multi-agent settings.","pith_inferences":["These results suggest normative judgments about AI information-hiding should be made at the policy or communication level rather than at the level of individual actions; the same visible suppression can be benign or harmful depending on whether the human can infer the assistant's policy.","The entropy-minimization proof points to a concrete design rule: among optimal assistant policies, choose the one minimizing the expected posterior entropy of the human's state belief, which yields non-interference at the policy level.","If future assistants use such suppression, transparency about the assistant's policy could convert seemingly harmful interference into legitimate communication, for example by announcing that information is being hidden because it is irrelevant or incorrect.","The gap between finite and continuous POAGs means Theorem 4.7 may not hold for continuous-state settings, and checking that extension would refine the theory beyond what the paper proves."],"forward_implications":["Action-level observation interference can appear in optimal solutions even with a perfectly aligned assistant and a human who observes and acts naively.","There is always an optimal solution without policy-level interference, so the assistant's hidden actions function as a communication device rather than a necessary manipulation.","Adding an unbounded assistant-to-human communication channel removes the first incentive (Theorem 4.5), and a two-way channel restores non-interference under naive human behavior (Theorem 5.3).","If the human is Boltzmann-rational, suppressing information can improve decisions, and for every positive rationality parameter there exists a POAG where all optimal policy pairs interfere with observations.","Experimental results in a product-selection game show that more assistant private information strengthens the incentive to interfere, while more human rationality weakens it."],"supporting_citations":[{"why":"Defines assistance games and the partially observable assistance game model this paper builds on.","marker":"(Shah et al., 2020)"},{"why":"Supplies the informativeness order on experiments used to define observation interference.","marker":"(Blackwell, 1953)"},{"why":"States the classic nonnegative value of information result that the paper's policy-level theorem extends.","marker":"(Koller & Friedman, 2009)"},{"why":"Introduces cooperative inverse reinforcement learning, the shared-reward human-AI setting from which assistance games derive.","marker":"(Hadfield-Menell et al., 2016)"},{"why":"Provides the Boltzmann (logit) choice model used to formalize human irrationality.","marker":"(Luce, 1959)"},{"why":"Shows partial observability in reward learning can create deception incentives, the contrast motivating this paper's aligned-assistant analysis.","marker":"(Lang et al., 2024)"}],"fun_headline_variants":["AI assistants may need to hide info from humans at times","Action-level secrecy unavoidable for optimal aligned AI","Sometimes hiding observations is the ethical AI choice","Policy-level honesty always possible despite action-level hiding","Observation interference: necessary act, avoidable strategy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof of the no-policy-level-interference theorem assumes discrete state and observation spaces so that a Shannon entropy minimizer among optimal policies exists, while the theorem is stated without that restriction.","fun_headline_variants_meta":{"raw":{"variants":["AI assistants may need to hide info from humans at times","Action-level secrecy unavoidable for optimal aligned AI","Sometimes hiding observations is the ethical AI choice","Policy-level honesty always possible despite action-level hiding","Observation interference: necessary act, avoidable strategy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00018,"raw_usage":{"total_tokens":1327,"prompt_tokens":992,"completion_tokens":335,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":264}},"tokens_in":608,"tokens_out":335,"duration_ms":7712,"temperature":1.0,"reasoning_tokens":264,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:10:55.196360+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run an exhaustive search over optimal policy pairs in the formal finite POAG of Example 4.3 (Appendix B.3); the paper's Theorem 4.7 predicts at least one optimal pair is non-interfering at the policy level, so finding that every optimal pair interferes at the policy level under Definition 4.6 would disprove the theorem.","supporting_citations":[{"cited_title":"D., Abbeel, P., Dragan, A., and Russell, S","cited_arxiv_id":null,"evidence_quote":"Defines assistance games and the partially observable assistance game model this paper builds on."},{"cited_title":"Equivalent comparisons of experiments","cited_arxiv_id":null,"evidence_quote":"Supplies the informativeness order on experiments used to define observation interference."},{"cited_title":"and Friedman, N","cited_arxiv_id":null,"evidence_quote":"States the classic nonnegative value of information result that the paper's policy-level theorem extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Boltzmann (logit) choice model used to formalize human irrationality."},{"cited_title":"When Your AIs Deceive You: Challenges of Partial Observability in Reinforcement Learning from Human Feedback","cited_arxiv_id":"2402.17747","evidence_quote":"Shows partial observability in reward learning can create deception incentives, the contrast motivating this paper's aligned-assistant analysis."}],"review_version":1}