{"id":"2e59ce9b-fca9-45c3-8b3f-7c404ea0e851","arxiv_id":"2505.21974","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A learned Transformer-based acquisition policy for multi-objective Bayesian optimization, trained on synthetic Gaussian processes, achieves best or near-best hypervolume on most tested synthetic and 3D Gaussian Splatting tuning tasks without retraining.","lead":"BOFormer uses a Transformer trained by reinforcement learning to decide which point to test next in multi-objective Bayesian optimization, and reports zero-shot transfer to new problems without retraining. The idea is to include the history of past queries and a learned Q-value in the decision input, fixing a failure mode that arises when the same candidate point yields different hypervolume gains in different histories.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The compressed history in Eq. (5) omits queried locations and observed objective values, and the appended Q-bar token is a deterministic function of that same compressed history, so it cannot restore the missing information; the claimed resolution of the hypervolume identifiability issue is…","rationale":"The reader's CONDITIONAL verdict is appropriate, and the condition should remain. The most load-bearing issue is not the wording of the abstract, though the abstract is indeed too strong given Table 1; it is whether BOFormer's input representation can support the non-myopic Q-function it claims. Proposition 3.1 is correct for full histories, yet the method deliberately replaces full histories with the compressed sequence in Eq. (5). Adding Q-bar to the representation cannot by itself recover the queried locations and observed values, because Q-bar is the output of the same target network evaluated on the same compressed sequence. Thus the identifiability failure in Figure 1 is mitigated only heuristically. This matters because the paper's central novelty is presented as systematically addressing the identifiability issue; if the representation is not sufficient, the method is a trained heuristic whose edge could come from the training distribution, the demo policy, or the window size w=31, exactly the confounds the reader flags. The proposed concrete test searches for a pair of histories with identical BOFormer inputs but different optimal returns; if found, it falsifies the sufficiency claim. I do not recommend REJECT because the empirical results on both synthetic and HPO-3DGS still support BOFormer as a useful heuristic, and the public code makes the check feasible. The table-vs-abstract mismatch reinforces CONDITIONAL but is not the core structural weakness.","tokens_in":24829,"tokens_out":15324,"duration_ms":171915,"concrete_test":"Using the released code, fix K=2, a small discrete domain such as |X|=8, and a short horizon T=3. Search over GP prior hyperparameters and observation histories for two episodes whose BOFormer inputs at time t=2 are identical (same μ_j(x_j), σ_j(x_j), y_{j-1}^*, r_j for j<2, and hence identical Q-bar tokens from the frozen target network) but whose optimal two-step cumulative HV reward, computed by exhaustive enumeration of the finite environment, differs. If such a pair exists, the map in Eq. (5) is not injective and no deterministic Q can be the generalized Q*, falsifying the identifiability claim. If the search finds no pair, extend the same check to t=3 and report the result; either way, the experiment directly tests representational sufficiency.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Proposition 3.1 justifies Generalized DQN for the full history H_t, but BOFormer's policy is a function of the fixed-dimensional summary h_t in Eq. (5) together with o_t(x). For the learned Q to be the generalized Q*, the map from full history to (h_t, o_t(x)) must preserve all information relevant to future hypervolume improvement. This sufficiency is not proved, and the components of h_t strongly suggest it fails: h_t stores only the predictive mean and standard deviation at each previously selected point, the best-so-far vector y_{j-1}^*, the normalized reward r_j, and a Q-bar token. It does not store the queried locations x_j or the observed values y_j. Because Q-bar is computed by the target network from the same compressed inputs, it is a deterministic function of information already present and cannot inject the missing observations. Consequently, two runs with different GP posteriors can in principle produce identical BOFormer inputs but different optimal future HV improvements; no function of the BOFormer input can represent Q* in such cases. The paper's Figure 1 demonstrates identifiability failure only for the representation without Q; no analogous guarantee, invariant, or bound is given for the Q-augmented compressed representation. This is the load-bearing gap: the central novelty is presented as systematically resolving the identifiability issue, but the resolution is heuristic and may be an artifact of the training distribution, the history window w=31, and the demo policy.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes BOFormer, a Transformer-based deep Q-network for multi-objective Bayesian optimization (MOBO). It formulates MOBO as non-Markovian RL, uses a generalized DQN loss over histories, and compresses each history into a fixed-dimensional sequence of posterior statistics, best-so-far values, rewards, and target-network Q-values. The policy selects the point maximizing the learned Q-value. BOFormer is trained solely on synthetic GP functions and evaluated zero-shot on synthetic benchmarks and a new 3D Gaussian Splatting hyperparameter optimization dataset. The paper claims to be the first RL-based acquisition function for MOBO and claims to systematically resolve the hypervolume identifiability issue while consistently outperforming rule-based and learning-based baselines.","tokens_in":25147,"tokens_out":6600,"duration_ms":63740,"significance":"The contribution is potentially significant: a learning-based, domain-agnostic, non-myopic acquisition function for MOBO with zero-shot transfer would be a useful advance, and the paper provides broad empirical coverage, public code, and a new HPO-3DGS dataset. The Generalized DQN framing is sound, and the ablations on the demo policy, sequence length, and transfer across numbers of objectives are informative. However, the central theoretical claim about resolving the identifiability issue is not established for the compressed representation, and the empirical claim of consistent superiority is not supported by the reported tables. The paper warrants a major revision rather than acceptance in its current form.","major_comments":[{"comment":"The abstract's claim that BOFormer 'constantly outperforms' the benchmark algorithms is contradicted by the reported numbers. In Table 1, BOFormer attains 0.4476 on BC versus 0.4773 for qNEHVI, 0.9461 on DRa versus 0.9573 for NSGA-II, and 0.8642 on Matern versus 0.8696 for qNEHVI; in Table 2, BOFormer attains 0.8816 on Mic versus 0.8871 for FSAF. The text later hedges to 'largest or among the largest' (Section 5). The load-bearing claim of consistent outperformance should be replaced with a precise statement of where and by how much BOFormer wins, together with the associated statistical evidence.","section":"Abstract and §5, Tables 1–2"},{"comment":"The main results are reported as point estimates without error bars or confidence intervals, despite being averages over 100 evaluation episodes. This is not a purely cosmetic issue: on many tasks the differences between BOFormer and qNEHVI are around 1% (e.g., AR, RBF, BCD in Table 1; Chairs, Lego, Materials in Table 2), which is precisely the threshold used for bold/underline formatting. Performance profiles are shown only for a subset of tasks in Figure 3 and the appendix. The authors should report standard errors or bootstrap intervals for all tasks and perform a paired comparison (e.g., Wilcoxon signed-rank or performance-profile analysis) to support the claimed superiority.","section":"§5, Tables 1–2 and Figure 3"},{"comment":"The theoretical justification only covers full histories: Proposition 3.1 characterizes Q* for histories H_t, and Figure 1 demonstrates the identifiability failure for an observation representation without the Q-augmented token. However, BOFormer's policy is a function of the fixed-dimensional summary h_t in Eq. (5), which stores posterior means and standard deviations at past selected points, the best-so-far vector, normalized rewards, and a Q-bar token. It does not store the queried locations x_j or the observed values y_j, and Q-bar is itself computed by the target network from the same compressed inputs, so it cannot inject information absent from h_t. No theorem, invariant, or bound establishes that this compressed representation preserves all information relevant to future hypervolume improvement. Two runs with different GP posteriors can in principle yield identical BOFormer inputs but different optimal future improvements, in which case no function of the BOFormer input can represent Q*. The claim that BOFormer 'systematically addresses' the identifiability issue is therefore not supported; at present this resolution is heuristic, and its success may depend on the training distribution and window size. The authors should either prove sufficiency for a well-defined class of environments, or explicitly downgrade the claim and provide evidence that the failure cases are rare in the tested distribution.","section":"§3.2–§4.2, Eq. (5), Figure 1"},{"comment":"The history window w=31 is selected by an ablation on DRa, RBF, and Matern52 (Figure 4), which are the same test functions used in Table 1. Selecting hyperparameters on the evaluation tasks can inflate the reported performance and makes the zero-shot claim less clean. Please move the window-size selection to a separate validation set drawn from the training distribution (e.g., held-out synthetic GP functions) and report the final configuration with that protocol.","section":"§5, Figure 4 and Appendix A.2"}],"minor_comments":[{"comment":"The abstract's 'constantly outperforms' conflicts with Section 5's 'largest or among the largest'; please harmonize the wording.","section":"Abstract and §5"},{"comment":"The definition of y(i)*_t contains a typo ('y(i)_i' instead of 'y(i)_j'), and the history in Eq. (5) uses y(i)*_{j-1}; make the index convention explicit.","section":"§4.2, Eq. (5)"},{"comment":"The abstract states 68,000 parameters for HPO-3DGS while the main text says 'dense-grid searching 1440 hyperparameters'; clarify whether 1440 refers to hyperparameter configurations per scene and how the 68,000 figure is derived.","section":"Abstract and §5"},{"comment":"The loss in Algorithm 1 uses the notation Qb_bθ and Qb_¯θ without defining the superscript b; define it in the caption or surrounding text.","section":"Appendix C.1, Algorithm 1"},{"comment":"The text says 'first learning-based solution to MOBO' while the introduction claims 'first RL-based AF for MOBO'; the former is broader and should be qualified.","section":"§2.2"},{"comment":"The heading 'per-sample inference time' is ambiguous; specify that it is time per acquisition-function evaluation or query.","section":"Table 3"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is the first learning-based acquisition function for multi-objective BO, and that alone makes it worth a look. The Generalized DQN framing, the Q-augmented observation, and the cross-domain zero-shot transfer are all real contributions, backed by a wide benchmark set including high-dimensional synthetic problems and a 3DGS hyperparameter-tuning task. The code is public, and the training-on-synthetic/deploy-on-unseen setup is honest and reproducible in spirit.\n\nThe soft spots are real but not fatal. The abstract says \"constantly outperforms,\" yet their own Tables 1 and 2 show BOFormer loses to qNEHVI on Branin-Currin (0.4476 vs 0.4773) and to NSGA-II on Dixon-Rastrigin (0.9461 vs 0.9573), and it ties or nearly ties several baselines on RBF and Matern. The headline tables also lack error bars; the performance profiles in the appendix are more convincing, but they are not in the main text. The window size w=31 is chosen via ablation on the same test functions, which leaks test information into the hyperparameter choice.\n\nThe deeper issue is the identifiability claim. The stress-test note is correct: the history h_t in Eq. (5) stores the posterior mean and std at previously selected points, the best observed values, the normalized reward, and a Q-bar token. It does not store the queried locations x_j or the raw observed y_j, and Q-bar is a deterministic function of the same compressed history, so it cannot inject the missing information. The paper shows an identifiability failure for the representation without Q, but gives no theorem or bound for the Q-augmented version. That is a genuine gap between the \"systematically addresses\" language and what is actually shown. It does not refute the empirical method, which seems to work well on the tested distributions, but it means the paper's central narrative is stronger than its evidence.\n\nOne mild circularity worth noting: qNEHVI is both a leading baseline and the demo policy that seeds BOFormer's training data. The ablation shows a qNEHVI demo helps more than an NSGA-II demo, so the comparison to qNEHVI is not fully neutral. Reproducibility is also slightly undercut by no commit hash and unclear public availability of the HPO-3DGS dataset.\n\nNet: this is a serious paper with a novel idea and substantial experiments. It deserves a rigorous referee, and I would send it to review. The revisions I would demand: tone down the abstract, add error bars to the main tables, move the window-size ablation to a validation set, and either prove or explicitly qualify the identifiability resolution. As it stands, the empirical case for BOFormer is decent but the framing oversells it.","headline":"First RL-based acquisition function for MOBO with a genuinely novel Q-augmented history representation and broad zero-shot experiments, but the abstract overclaims and the paper's central identifiability fix rests on a heuristic rather than a proof.","tokens_in":25722,"tokens_out":2647,"would_cite":true,"duration_ms":28061,"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":"BOFormer, a Transformer Q-network trained on synthetic functions, is presented as the first RL-learned acquisition function for multi-objective Bayesian optimization, beating handcrafted rules and prior learned methods without fine-tuning.","keywords":["multi-objective Bayesian optimization","acquisition function learning","non-Markovian reinforcement learning","deep Q-learning","Transformer sequence modeling","hypervolume improvement","zero-shot transfer","3D Gaussian Splatting hyperparameter optimization"],"falsifier":"Build the pair of scenarios from the paper's motivating example: a candidate point whose posterior statistics and best-observed values are identical in the two settings, but whose hypervolume improvement upon sampling differs because the earlier histories differ, and ask BOFormer to score that point in both settings. If the learned Q-values coincide, the representation has not encoded history in exactly the case the paper says it fixes; a complementary stress test would check whether BOFormer's margin over qNEHVI collapses when the training lengthscales are drawn from a wider range than the paper's [0.1, 0.4].","tokens_in":24601,"feed_emoji":"🎯","tokens_out":28866,"duration_ms":230004,"temperature":0.7,"pith_summary":"The paper claims that multi-objective Bayesian optimization can be recast as a non-Markovian reinforcement-learning problem, and that a Transformer-based deep Q-network trained only on synthetic Gaussian-process functions learns a general-purpose acquisition function that beats handcrafted rules and prior learned methods on synthetic benchmarks and on real hyperparameter tuning for 3D Gaussian Splatting rendering. The obstacle it targets is the hypervolume identifiability issue: the benefit of a query, measured by the increase in hypervolume (the volume of objective space dominated by the samples collected so far), depends on the whole history of previous samples, so a policy fed only current posterior statistics cannot tell whether a move is good. BOFormer feeds a Transformer the sequence of past observation-action pairs, describes each candidate point by its posterior mean and uncertainty, the best values seen so far, the remaining budget, and the network's own predicted Q-value, and selects the point with the maximal Q-value. If the claim holds, non-myopic multi-objective acquisition becomes a single forward pass of a learned network, with inference cost nearly flat in the number of objectives and zero-shot transfer across domains and dimensions.","feed_headline":"A trained policy beats handcrafted rules in multi-objective search","feed_subtitle":"Trained on synthetic functions alone, it tunes real 3D rendering pipelines better than expert solvers.","key_machinery":"The load-bearing object is the generalized optimal Q-function on histories, $Q^*(h,a)$, defined by the non-Markovian Bellman optimality equation $Q(h,a) = \\mathbb{E}_{o \\sim p(\\cdot|h,a)}[r(h,a,o) + \\gamma \\max_{a'} Q(h', a')]$ with $h' = (h,a,o)$, which the paper imports from the general-RL literature and turns into a temporal-difference loss with a frozen target network. BOFormer approximates this Q-function with a GPT-2-style Transformer that consumes the sequence of past per-point observation-action tokens; the crucial augmentation is that each observation carries its own Q-value from the target network, which acts as a learned summary of the prospective hypervolume improvement and keeps the token size constant as the domain grows. The reward is the normalized hypervolume improvement $r_t = (HV(X_t) - HV(X_{t-1}))/(HV(X^{*}) - HV(X_t))$, which keeps the learning signal strong late in an episode, and the fixed history window ($w = 31$) supplies the context that posterior statistics alone provably lack. The action-selection rule carries the argument: at each step the query is $x_t = \\arg\\max_{x \\in X} Q_{\\hat{\\theta}}(h_t, o_t(x))$.","core_discovery":"The paper's central claim is that the history-dependence of hypervolume improvement, which makes multi-objective Bayesian optimization non-Markovian in a way single-objective BO is not, can be handled by learning a generalized optimal Q-function over histories rather than over states, and that this yields a working acquisition function. It formalizes the idea as Generalized DQN, built on the non-Markovian Bellman optimality equation, and implements it as BOFormer, a GPT-2-style Transformer that consumes a sequence of per-step observation-action tokens and outputs Q-values. The decisive design choice is the Q-augmented representation: each candidate point $x$ is encoded as $o_t(x) = (\\mu_t^{(i)}(x), \\sigma_t^{(i)}(x), y_t^{(i)*}, t/T)$ over objectives $i$, augmented with the Q-value produced by a frozen target network, and the chosen point is $x_t = \\arg\\max_{x \\in X} Q_{\\hat{\\theta}}(h_t, o_t(x))$ with $h_t$ the history of past observation-action pairs. Because each token describes one candidate point and its size does not grow with the domain size, the model transfers across domains and dimensions and avoids the memory blow-up of a direct full-state implementation. Trained on randomly drawn GP functions with a normalized hypervolume-improvement reward, guided partly by an expected-hypervolume-improvement demo policy and replayed from a prioritized trajectory buffer, BOFormer is deployed without fine-tuning; the authors report that it attains the largest or near-largest hypervolume at the final sampling step on the synthetic benchmarks and on a 3D Gaussian Splatting hyperparameter-tuning dataset.","pith_inferences":["The Q-augmented observation is self-referential: the appended value is an output of the same network being trained, so it is informative only to the extent the policy has already learned, and early in training it cannot help identify history-dependent improvements. A testable consequence is that the method's edge over expected-hypervolume-improvement baselines should shrink if the Q-augmentation i","The window length is a fixed hyperparameter ($w = 31$), making the method approximate, not exact, in its non-Markovianity; a natural stress test is to check whether the window must grow with the number of objectives or with the GP lengthscale, since longer-range posterior correlations should make more distant history relevant.","The training-time reward normalizes by the optimal hypervolume $HV(X^{*})$ of the synthetic training functions, a quantity unavailable at deployment; this makes the training distribution the carrier of that information, and the policy's behavior on tasks whose Pareto front is hard to estimate is an open question the benchmarks do not fully settle.","The Generalized DQN machinery is not specific to hypervolume: other acquisition problems with history-dependent utility, such as batch acquisition where the value of a point depends on the other points chosen alongside it, or constrained BO where past queries affect future feasibility, could be cast in the same sequence-modeling form."],"forward_implications":["Multi-objective acquisition becomes a cheap forward pass: reported per-step inference time is roughly constant (about 14 ms) for 2, 3, and 4 objectives, whereas qNEHVI grows from about 6 ms to 224 ms, so the learned rule is the cheaper option as the number of objectives grows.","Zero-shot and cross-domain deployment is claimed: the same weights trained only on synthetic GP functions produce competitive hypervolumes on 10-, 30-, 40-, and 100-dimensional test problems and on the real 3D Gaussian Splatting tuning task, without fine-tuning or task metadata.","The appended Q-value is the load-bearing piece of the representation: Q-Transformer, which uses the same temporal-difference sequence modeling without the Q-augmented observation, performs noticeably worse, isolating the paper's key design choice.","History is doing real work: the ablation across sequence lengths shows that variants with $w > 1$ beat the Markovian variant with $w = 1$, supporting the diagnosis that the improvement signal is history-dependent.","The paper positions BOFormer as the first RL-based acquisition function for multi-objective Bayesian optimization, extending the learned-acquisition paradigm from the single-objective setting where FSAF-style methods worked to the multi-objective setting where their direct extension fails."],"supporting_citations":[{"why":"Supplies the generalized Bellman optimality equations for non-Markovian RL that the Generalized DQN loss in Proposition 3.1 is built on.","marker":"(Dong et al., 2022)"},{"why":"DQN is the algorithm being generalized; BOFormer's temporal-difference loss with a frozen target network is its non-Markovian analogue.","marker":"(Mnih et al., 2013)"},{"why":"FSAF is the single-objective RL acquisition function whose naive extension to MOBO exhibits the hypervolume identifiability issue of Figure 1, and it serves as a learning-based baseline.","marker":"(Hsieh et al., 2021)"},{"why":"Defines expected hypervolume improvement, the demo policy that guides training exploration and the quantity the paper's reward is built around.","marker":"(Emmerich & Klinkenberg, 2008)"},{"why":"qNEHVI is the strongest rule-based baseline and the concrete demo policy used in training; the headline comparisons are measured against it.","marker":"(Daulton et al., 2021)"},{"why":"Decision Transformer provides the sequence-modeling template for mapping histories to decisions and is adapted as a learning-based baseline.","marker":"(Chen et al., 2021)"},{"why":"Q-Transformer is the control variant that differs from BOFormer mainly by lacking the Q-augmented observation, isolating the key design choice.","marker":"(Chebotar et al., 2023)"},{"why":"MetaBO contributes the Sobol-grid maximization BOFormer uses for continuous domains and is prior RL-based acquisition-function work.","marker":"(Volpp et al., 2020)"},{"why":"3D Gaussian Splatting is the real-world testbed; the HPO-3DGS dataset and tuning benchmark are built on it.","marker":"(Kerbl et al., 2023)"}],"fun_headline_variants":["Transformer RL policy outlearns handcrafted rules in multi-objective BO","BOFormer: sequence-modeled Q-learning for multi-objective optimization","Non-Markovian RL rethinks acquisition functions for MOBO","Deep Q-learning with history beats myopic heuristics in MOBO","GPT-style policy for hypervolume improvement in multi-objective BO"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole scheme rests on the assumption that a fixed-size summary — each candidate point's posterior statistics, a window of the last 31 decisions, and the network's own predicted Q-value — captures enough of the sampling history to tell the policy what the next query is worth; the paper verifies this empirically on its benchmarks but provides no guarantee that this summary identifies the hypervolume improvement in general.","fun_headline_variants_meta":{"raw":{"variants":["Transformer RL policy outlearns handcrafted rules in multi-objective BO","BOFormer: sequence-modeled Q-learning for multi-objective optimization","Non-Markovian RL rethinks acquisition functions for MOBO","Deep Q-learning with history beats myopic heuristics in MOBO","GPT-style policy for hypervolume improvement in multi-objective BO"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000222,"raw_usage":{"total_tokens":1520,"prompt_tokens":1077,"completion_tokens":443,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":693,"completion_tokens_details":{"reasoning_tokens":350}},"tokens_in":693,"tokens_out":443,"duration_ms":4524,"temperature":1.0,"reasoning_tokens":350,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:19:22.130844+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build the pair of scenarios from the paper's motivating example: a candidate point whose posterior statistics and best-observed values are identical in the two settings, but whose hypervolume improvement upon sampling differs because the earlier histories differ, and ask BOFormer to score that point in both settings. If the learned Q-values coincide, the representation has not encoded history in exactly the case the paper says it fixes; a complementary stress test would check whether BOFormer's margin over qNEHVI collapses when the training lengthscales are drawn from a wider range than the paper's [0.1, 0.4].","supporting_citations":[{"cited_title":"Simple agent, complex environment: Efficient reinforcement learning with agent states","cited_arxiv_id":null,"evidence_quote":"Supplies the generalized Bellman optimality equations for non-Markovian RL that the Generalized DQN loss in Proposition 3.1 is built on."},{"cited_title":"Reinforced few-shot acquisition function learning for Bayesian optimization","cited_arxiv_id":null,"evidence_quote":"FSAF is the single-objective RL acquisition function whose naive extension to MOBO exhibits the hypervolume identifiability issue of Figure 1, and it serves as a learning-based baseline."},{"cited_title":"The computation of the expected improvement in dominated hypervolume of Pareto front approximations","cited_arxiv_id":null,"evidence_quote":"Defines expected hypervolume improvement, the demo policy that guides training exploration and the quantity the paper's reward is built around."},{"cited_title":"Parallel Bayesian optimization of multiple noisy objectives with expected hypervolume improvement","cited_arxiv_id":null,"evidence_quote":"qNEHVI is the strongest rule-based baseline and the concrete demo policy used in training; the headline comparisons are measured against it."},{"cited_title":"Decision Transformer: Reinforcement learning via sequence modeling","cited_arxiv_id":null,"evidence_quote":"Decision Transformer provides the sequence-modeling template for mapping histories to decisions and is adapted as a learning-based baseline."},{"cited_title":"Q-Transformer: Scalable offline reinforcement learning via autoregressive q-functions","cited_arxiv_id":null,"evidence_quote":"Q-Transformer is the control variant that differs from BOFormer mainly by lacking the Q-augmented observation, isolating the key design choice."},{"cited_title":"Meta-learning acquisition functions for transfer learning in Bayesian optimization","cited_arxiv_id":null,"evidence_quote":"MetaBO contributes the Sobol-grid maximization BOFormer uses for continuous domains and is prior RL-based acquisition-function work."}],"review_version":1}