{"id":"96f410d7-24f0-4786-8569-52fe8966be47","arxiv_id":"2411.12878","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A new 'Local Anti-Concentration' condition on context distributions lets the pure-greedy linear contextual bandit algorithm achieve O(poly log T) expected regret for distributions beyond Gaussian and uniform, including Laplace, exponential, and truncated heavy-tailed laws.","lead":"This paper proves that a simple 'always pick the best-looking option' bandit algorithm can still learn efficiently over time, as long as the context features come from a broad family of continuous distributions it calls the Local Anti-Concentration class. The result widens the known settings where exploration-free algorithms are provably efficient, with regret growing only logarithmically in the time horizon.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"LAC alone does not imply poly-log regret: Theorem 1 requires Assumption 2 (ψ1-boundedness), which the advertised Cauchy and Student's t examples violate; untruncated Cauchy even has infinite expected reward.","rationale":"The reader's weakest-assumption analysis identifies exactly this issue: Assumption 2 is load-bearing and is violated by the heavy-tailed laws highlighted in the abstract. I agree, and I add that the problem is even sharper for Cauchy, where expected regret is not finite, so no finite-regret theorem can hold for the untruncated distribution. The paper's internal proof appears consistent under Assumption 2, and the theorem statement itself is explicit about that assumption; hence this is a scope and framing defect rather than a demonstrated internal contradiction in the proof. Because the advertised breadth is a central contribution, the abstract and Table 1 should be revised to state that the regret guarantee covers LAC distributions that are bounded or ψ1-bounded, with heavy-tailed cases handled only after truncation. This supports the reader's CONDITIONAL verdict without changing it.","tokens_in":91830,"tokens_out":11708,"duration_ms":126173,"concrete_test":"Independently compute ∥X∥ψ1 for untruncated Cauchy and Student's t: sup_{p≥1} p^{-1} E^{1/p}|X|^p is infinite in both cases. Then revisit Appendix G.2.1 with the Cauchy tail P(|X|>R) ~ 1/R: the required inequality P(X∈D^K) ≥ 1/2 fails for the logarithmic R1 used in Claim 4, and for Cauchy E|X|=∞ makes the paper's expected regret infinite. This settles whether the advertised Cauchy/Student's t coverage is a theorem or a truncation artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weakness is that the poly-log guarantee is not a property of the LAC condition alone: it depends essentially on Assumption 2. In Appendix G.2.1, the truncation radius is R1 = c0 xmax(log d + log K + 2), and Claim 4 relies on a sub-exponential tail bound P(|X_ij| > R1) ≤ 1/(2dK), which requires the ψ1 norm to be finite and at most xmax. The examples advertised in the abstract — Cauchy and Student's t — do not satisfy this. For Cauchy, E|X| is infinite, so ∥X∥ψ1 = sup_{p≥1} p^{-1} E^{1/p}|X|^p is infinite. For Student's t with ν degrees of freedom, moments exist only for p < ν, so the supremum over all p ≥ 1 is also infinite. More fundamentally, for untruncated Cauchy contexts, E[X_a^T θ*] is infinite, so the expected regret in the paper's definition is not well-defined and cannot be finite for any algorithm. Thus Theorem 1 is proved only for the strictly smaller class 'LAC ∩ {ψ1-bounded or bounded}', which is exactly what Table 1 lists as truncated Cauchy and truncated Student's t. The abstract's wording that the LAC condition covers Cauchy and Student's t and yields logarithmic regret is an overclaim that changes the practical scope of the central result. This does not falsify Theorem 1 under its stated assumptions, but it means the headline contribution — the breadth of the LAC class — is narrower than claimed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a Local Anti-Concentration (LAC) condition, a bound on the ∞-norm of the log-density gradient, and claims that for context distributions satisfying LAC, the exploration-free LinGreedy algorithm for linear contextual bandits enjoys O(poly log T) expected regret. The proof strategy is modular: LAC is used to bound the decay rate of densities, which yields a lower bound on the diversity constant λ⋆(t) (Theorem 2) and an upper bound on the margin constant C∆(t) (Theorem 3); these two ingredients are then combined with a standard regret decomposition to obtain the main result (Theorem 1). The paper also claims that the LAC class includes Gaussian, exponential, uniform, Cauchy, and Student's t distributions, together with many exponential-family and truncated variants.","tokens_in":92078,"tokens_out":9600,"duration_ms":104833,"significance":"If the main theorem is correct, this is a valuable contribution: it replaces earlier Gaussian- or uniform-specific analyses of greedy contextual bandits with a general density condition, and it derives rather than assumes the diversity and margin constants. The appendix gives a detailed, modular proof with no fitted parameters, and the comparison with the earlier Gaussian √T bound of Kannan et al. provides a useful external anchor. The paper is also candid in places: Table 1 lists truncated Cauchy and truncated Student's t, and Appendix K records that Gibbs distributions fail the diversity condition for K ≥ 3. However, the abstract and Section 3.2 substantially overstate the scope of the regret theorem: the advertised untruncated heavy-tailed examples do not satisfy the assumptions under which the theorem is proved, and for untruncated Cauchy the paper's own regret definition is not even finite. The central derivation appears defensible under the stated assumptions, but the headline claims need to be narrowed and reworded.","major_comments":[{"comment":"The abstract and Section 3.2 state that the LAC class includes Cauchy and Student's t distributions and that 'under our proposed LAC condition' the greedy algorithm achieves O(poly log T) regret. However, Theorem 1 is proved only under Assumptions 1 and 2, and for unbounded contexts Assumption 2 requires a finite ψ1 norm. For Cauchy and for Student's t with any finite degrees of freedom, the ψ1 norm is infinite: for Student's t with ν degrees of freedom, E|X|^p is infinite for p ≥ ν, so the supremum in the definition of the ψ1 norm diverges. The truncation argument in Appendix G.2.1 and Claim 4, which are load-bearing for Theorem 2, rely on the sub-exponential tail bound that follows from a finite ψ1 norm. Table 1 correctly lists truncated Cauchy and truncated Student's t, but the abstract and Section 3.2 do not qualify the examples. The paper should explicitly state that the regret theorem applies to the class 'LAC ∩ {bounded or ψ1-bounded contexts}' and that the heavy-tailed examples are covered only in truncated form.","section":"Abstract, Section 3.2, Table 1, Section 5.1"},{"comment":"For untruncated Cauchy contexts, the expected regret as defined in Section 2.2 is not finite. If θ* has a nonzero component and Xi is Cauchy, then E|Xi| is infinite, so E[Xi(t)⊤θ*] is undefined and the expression Reg(T) = Σ_t E[X_a*(t)⊤θ* − X_a(t)⊤θ*] is not a finite quantity for any algorithm. Consequently, the abstract's inclusion of untruncated Cauchy among the distributions for which logarithmic regret is proved is incompatible with the paper's own regret definition. This is not a minor technicality: it means that the advertised heavy-tailed examples cannot be repaired by a sharper proof within the same problem formulation. The authors should either state that untruncated heavy-tailed examples are outside the scope of the regret guarantee or define a modified (e.g., truncated or otherwise regularized) regret notion.","section":"Section 2.2, Abstract"},{"comment":"The phrase 'under our proposed LAC condition' is stronger than what is shown. Theorem 1 requires not just LAC but also Assumption 1 (independence of context sets across rounds) and Assumption 2 (boundedness or ψ1-boundedness). The LAC condition alone is not sufficient for the regret conclusion, and in fact a density can satisfy LAC while having infinite first moments, so the paper should not present LAC as the sole enabling assumption. The theorem should be phrased as a result for the class 'LAC ∩ {Assumptions 1 and 2}', and the introduction and abstract should avoid the implication that the LAC condition by itself characterizes the distributions for which exploration-free greedy learning is efficient.","section":"Section 5.2, Section 3"}],"minor_comments":[{"comment":"The exponential density is written as f_X(x) = (1/λ) exp(−λx), which is missing the normalizing factor λ; the derivative calculation is unaffected, but the displayed density is incorrect.","section":"Section 3.2"},{"comment":"The last row, 'PDF f ∝ exp(−π) with polynomially growing π', is ambiguous because π is also used as a constant elsewhere; it should be written with a function such as V(x) or π(x).","section":"Table 1"},{"comment":"The discussion states λ⋆(t) ≥ Ω(1/d), but the displayed bound is c/(d (A1 + A2(R1+2)^α)^2), and A2(R1+2)^α can grow like a power of log d for unbounded contexts. The Ω(1/d) statement should be qualified as holding up to factors depending on L(R1) or should be restated as Ω(1/(d L(R1)^2)).","section":"Discussion of Theorem 2, Section 5.3.1"},{"comment":"There are numerous typographical errors ('Univeristy', 'simplicty', 'greey', 'wide rage', 'Dicussions') and the phrase 'sharp poly-logarithmic regret' is not supported by a lower bound. A careful proofreading pass and a more conservative choice of 'sharp' are recommended.","section":"Throughout"},{"comment":"The negative result for Gibbs distributions with K ≥ 3 is interesting and relevant to the paper's claimed scope; it appears only in a footnote and in the appendix, so it would be helpful to summarize this limitation in the main text when discussing the breadth of the LAC class.","section":"Appendix K"},{"comment":"The sentence 'Choose one of v, −v such that ⟨·, θ⟩ ≥ 0' is unclear notation; it should be written in terms of the sign of ⟨v, θ⟩ or ⟨−v, θ⟩.","section":"Proof of Claim 1, Appendix F.3.1"}],"recommendation":"major_revision","confidential_remarks":"The paper's central proof appears to be a substantial and largely coherent piece of work, and the distinction between the LAC condition and the additional ψ1-boundedness assumption is the key issue. The abstract and Section 3.2 overclaim coverage of untruncated heavy-tailed distributions, and for Cauchy the regret definition itself is not finite. These are presentation-and-scope problems rather than errors in the core derivation under the stated assumptions, so major revision rather than rejection seems appropriate. The authors should also be asked to check whether Table 1 and the abstract can be made consistent about which distributions are covered only after truncation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The LAC condition is a real contribution. It gives a checkable distributional criterion that covers Laplace, exponential, uniform, generalized exponential families, and truncated heavy-tailed laws, and the paper proves poly-log regret for greedy selection under it. That is genuinely new, and it goes beyond the prior Gaussian/uniform straitjacket. Even better, the margin constant and diversity constant are derived from the density, not assumed the way Bastani et al. do. The proof chain — LAC gives a bounded decay rate, which feeds section-density lemmas bounding lambda* and C_delta — is coherent and, as far as I can check, supported by the appendices. No fitted parameters, no obvious circularity. The honest treatment of limitations (Appendix K on discrete contexts, Gibbs failing for K >= 3) also counts in its favor.\n\nThe soft spots are real but not fatal. First, the abstract overclaims. It lists Cauchy and Student's t as distributions under which the greedy algorithm achieves logarithmic regret. But Theorem 1 requires Assumption 2 (psi1-boundedness), and untruncated Cauchy and Student's t violate that. For untruncated Cauchy the first moment is infinite, so the expected regret in the paper's own definition is not well-defined; no algorithm can have finite expected regret there. Table 1 quietly fixes this by listing truncated versions, and the theorem itself is fine, but the abstract's framing changes the practical scope. That needs to be corrected. Second, the paper sometimes writes as if LAC alone implies the regret bound, but the guarantee really is for LAC ∩ {psi1-bounded or bounded}; the stress-test note got this right. Third, the d-dependence needs a careful pass: G.4's displayed bound appears to have an extra power of d that doesn't obviously give the eO(d^2.5) stated in Theorem 1. That may just be sloppy hiding of logs, but a referee should pin it down. Fourth, the experiments are single seeds without error bars, which is fine for sanity checks but not evidence. Finally, I could not mechanically verify the bounded-context geometric lemmas (16 and 17); they are dense and the figures are doing a lot of work.\n\nWho is this for? Anyone working on exploration-free bandits, smoothed linear bandits, or stochastic linear bandits more generally. It deserves a serious referee: the main theorem is important enough and the proof structure is detailed enough that a careful audit is worth the time. Send it to review, with instructions that the abstract overclaim and the d-dependence in G.4 must be fixed.","headline":"Genuine step forward for greedy linear contextual bandits, but the abstract oversells untruncated heavy-tailed contexts; the real theorem needs psi1-boundedness, and for Cauchy the regret isn't even defined.","tokens_in":92726,"tokens_out":2493,"would_cite":true,"duration_ms":30135,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62L05","68W27"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper proves that one condition on the context distribution — no sharp log-density growth — makes an exploration-free greedy bandit algorithm achieve poly-logarithmic regret.","keywords":["linear contextual bandits","greedy algorithm","exploration-free","Local Anti-Concentration","logarithmic regret","margin condition","stochastic contexts"],"falsifier":"Run LinGreedy with two arms and small dimension on contexts drawn from an untruncated Cauchy distribution out to $T = 10^6$: if the cumulative regret follows a power law in $T$ rather than a poly-logarithmic curve, the $\\psi_1$ premise carries the theorem and the advertised Cauchy coverage holds only after truncation; if the regret stays poly-logarithmic, the theorem's tail assumption is stronger than necessary.","tokens_in":91500,"feed_emoji":"🎰","tokens_out":17502,"duration_ms":151138,"temperature":0.7,"pith_summary":"Pure exploitation, with no deliberate exploration, is enough to learn optimally in linear contextual bandits, provided the context distribution's log-density does not change too sharply anywhere. The paper introduces the Local Anti-Concentration (LAC) condition — $\\|\\nabla \\log f(x)\\|_\\infty$ bounded by a polynomial in $\\|x\\|_\\infty$ — and proves that under it the greedy algorithm LinGreedy achieves cumulative expected regret $O(\\mathrm{poly}\\log T)$, with dimension dependence $\\tilde{O}(d^{2.5})$ for unbounded contexts. This matters because exploration is often expensive, infeasible, or ethically fraught (healthcare is the recurring example), and previous efficiency guarantees for greedy bandits covered essentially only Gaussian and uniform contexts or required a separately assumed margin condition. Under LAC the two ingredients those earlier analyses assumed — growth of the selected-context Gram matrix's minimum eigenvalue and a probabilistic upper bound on the suboptimality gap — follow as theorems rather than assumptions. The LAC class contains Gaussian, exponential, uniform, Laplace, Cauchy, and Student's $t$ distributions and their truncated variants, the widest class of context distributions for which exploration-free bandits are known to be provably near-optimal.","feed_headline":"A single density condition gives greedy bandits polylog regret","feed_subtitle":"Pure exploitation now provably suffices for Gaussians, exponentials, Laplace, and truncated heavy tails.","key_machinery":"The Local Anti-Concentration (LAC) condition: a density $f$ satisfies it when $\\|\\nabla \\log f(x)\\|_\\infty \\le L(\\|x\\|_\\infty)$ for a non-decreasing polynomial $L$, a uniform control on how fast the log-density slopes upward that rules out sharp local concentration while still allowing heavy tails. Its load-bearing property is that it bounds the one-sided decay rate of every one-dimensional projection of the conditional distributions the greedy policy induces, and it is preserved under conditioning with the same function $L$, so conditioning on the event that arm $i$ is chosen does not break the hypothesis. Three lemmas convert decay rates into the constants the regret proof needs: a bounded one-sided decay rate forces a variance lower bound (Lemma 4) and a maximum-density upper bound (Lemma 5), and for sets with equal or expanding hyperplane sections the section density inherits the same decay (Lemma 8). Truncation to high-probability regions extends the analysis to unbounded contexts, a separate section-geometry argument covers naturally bounded contexts, and a peeling concentration argument then sums the per-round bounds into the final poly-logarithmic regret.","core_discovery":"The paper's central claim is that a single distributional condition simultaneously guarantees everything a greedy algorithm needs. Concretely: if the context distribution satisfies LAC with a polynomial $L$, Assumptions 1–2 hold (context sets independent across time; contexts bounded, or unbounded with bounded $\\psi_1$ norm), then LinGreedy — an OLS-based algorithm that always pulls the arm maximizing estimated reward and never explores — has cumulative expected regret $\\mathrm{Reg}(T) \\le O(\\mathrm{poly}\\log T)$, and for unbounded contexts the bound reads $\\tilde{O}(d^{2.5})$ with dependencies at most polynomial in $d$ and $K$ in the bounded case. The two constants that dominate greedy regret are derived, not assumed: the diversity constant $\\lambda_\\star(t) \\ge \\Omega(1/d)$ (Theorem 2) and the margin constant $C_\\Delta(t) \\le \\tilde{O}(\\sqrt{d})$ (Theorem 3), both following from LAC alone. The paper additionally states that the OLS estimator is $\\sqrt{t}$-consistent, $\\|\\hat\\theta_t - \\theta^\\star\\|_2 \\le \\tilde{O}(d/\\sqrt{t})$ with high probability, a property it notes that exploration-based UCB and Thompson sampling analyses do not generally provide.","pith_inferences":["My inference: because LAC is stated through the density's log-gradient, its certified class is continuous contexts; extending it to discrete or categorical features will need a new anti-concentration notion, and the paper's own appendix observes that Gibbs-style discrete distributions fail the diversity condition once $K \\ge 3$, so the extension is non-mechanical.","My inference: the $\\psi_1$ tail assumption is load-bearing rather than bookkeeping, since untruncated heavy-tailed contexts formally fall outside Theorem 1; replacing it by a polynomial-moment condition with a growing truncation radius is a plausible route, at the cost of larger dimension constants.","My inference: the mechanism — LAC survives conditioning, so every deterministic policy-induced distribution keeps its decay-rate bound — should transfer to other settings where actions are greedy functions of an estimated parameter, such as generalized linear bandits or greedy policy search.","My inference: the paper predicts graceful degradation as the LAC function $L$ grows, but not beyond it; a bounded-support density with super-polynomial log-slope (e.g., $f \\propto \\exp(-\\exp(x))$) sits outside the LAC class, and Theorem 2's diversity mechanism should measurably collapse there, a probe worth running."],"forward_implications":["For every context distribution in the LAC class, a pure greedy policy matches the regret order of exploration-based algorithms, removing the exploration-exploitation trade-off in deployments where exploration is costly or unwelcome.","The margin (low-noise) condition that earlier greedy-bandit analyses assumed becomes a derived consequence with explicit constants $C_\\Delta(t) \\le \\tilde{O}(\\sqrt{d})$.","The OLS estimator under adaptively chosen greedy contexts is $\\sqrt{t}$-consistent, which gives sample-complexity and PAC-type statements that standard UCB and Thompson sampling analyses do not deliver.","For bounded-support contexts the bound stays polynomial in $d$ and $K$ while remaining poly-logarithmic in $T$, so the guarantee does not silently degrade as the number of arms grows.","Gaussian, uniform, Laplace, exponential-family, and truncated heavy-tailed contexts (Cauchy, Student's $t$) are all certified, widening the provably admissible class well beyond the Gaussian and uniform pair."],"supporting_citations":[{"why":"The prior mostly exploration-free analysis this work extends; it assumed the diversity and margin conditions that the present paper derives from LAC, and it covered Gaussian and uniform (and, for two arms, Gibbs) contexts.","marker":"[8]"},{"why":"Provides the smoothed-analysis baseline of $\\tilde{O}(\\sqrt{T})$ regret for Gaussian contexts that Theorem 1 improves to polylog.","marker":"[20]"},{"why":"The second Gaussian-context smoothed-analysis baseline ($\\tilde{O}(\\sqrt{T})$ regret) whose distributional scope the LAC class widens.","marker":"[33]"},{"why":"The closest prior single-parameter greedy guarantee, a Bayesian-regret bound of $\\tilde{O}(T^{1/3})$ in smoothed settings, which the paper's frequentist polylog bound strengthens.","marker":"[30]"},{"why":"Self-normalized concentration inequalities that convert the diversity constant into the high-probability $\\ell_2$ estimation error bound used throughout the regret analysis.","marker":"[1]"},{"why":"The self-normalized process martingale theory supporting the $\\sqrt{t}$-consistency of the OLS estimator under adaptively chosen contexts.","marker":"[29]"},{"why":"The stochastic-context regret decomposition that turns the two challenge constants ($\\lambda_\\star(t)$ and $C_\\Delta(t)$) into a poly-logarithmic cumulative regret bound.","marker":"[7]"},{"why":"The linear-response bandit analysis whose peeling and margin techniques are adapted for the final regret summation over unbounded contexts.","marker":"[19]"},{"why":"Supplies the $\\psi_1$ sub-exponential concentration inequalities used to justify the truncation constructions for unbounded contexts.","marker":"[37]"}],"fun_headline_variants":["Greedy bandits get polylog regret via one density condition","Local anti-concentration: greedy without exploration achieves polylog","One density condition turns greedy contextual bandits polylog-regret","Greedy linear contextual bandits: polylog regret under LAC condition"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For unbounded contexts the proof rests on Assumption 2, which requires the context vectors to have a finite $\\psi_1$ (sub-exponential) norm, so genuinely heavy-tailed laws such as untruncated Cauchy or Student's $t$ lie outside the theorem's formal scope and are covered only in truncated form.","fun_headline_variants_meta":{"raw":{"variants":["Greedy bandits get polylog regret via one density condition","Local anti-concentration: greedy without exploration achieves polylog","One density condition turns greedy contextual bandits polylog-regret","Greedy linear contextual bandits: polylog regret under LAC condition"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001037,"raw_usage":{"total_tokens":4380,"prompt_tokens":976,"completion_tokens":3404,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":592,"completion_tokens_details":{"reasoning_tokens":3326}},"tokens_in":592,"tokens_out":3404,"duration_ms":24723,"temperature":1.0,"reasoning_tokens":3326,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:09:14.300857+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run LinGreedy with two arms and small dimension on contexts drawn from an untruncated Cauchy distribution out to $T = 10^6$: if the cumulative regret follows a power law in $T$ rather than a poly-logarithmic curve, the $\\psi_1$ premise carries the theorem and the advertised Cauchy coverage holds only after truncation; if the regret stays poly-logarithmic, the theorem's tail assumption is stronger than necessary.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The prior mostly exploration-free analysis this work extends; it assumed the diversity and margin conditions that the present paper derives from LAC, and it covered Gaussian and uniform (and, for two arms, Gibbs) contexts."},{"cited_title":"H., Roth, A., Waggoner, B., and Wu, Z","cited_arxiv_id":null,"evidence_quote":"Provides the smoothed-analysis baseline of $\\tilde{O}(\\sqrt{T})$ regret for Gaussian contexts that Theorem 1 improves to polylog."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The second Gaussian-context smoothed-analysis baseline ($\\tilde{O}(\\sqrt{T})$ regret) whose distributional scope the LAC class widens."},{"cited_title":"W., and Wu, Z","cited_arxiv_id":null,"evidence_quote":"The closest prior single-parameter greedy guarantee, a Bayesian-regret bound of $\\tilde{O}(T^{1/3})$ in smoothed settings, which the paper's frequentist polylog bound strengthens."},{"cited_title":"H., Lai, T","cited_arxiv_id":null,"evidence_quote":"The self-normalized process martingale theory supporting the $\\sqrt{t}$-consistency of the OLS estimator under adaptively chosen contexts."},{"cited_title":"and Bayati, M","cited_arxiv_id":null,"evidence_quote":"The stochastic-context regret decomposition that turns the two challenge constants ($\\lambda_\\star(t)$ and $C_\\Delta(t)$) into a poly-logarithmic cumulative regret bound."},{"cited_title":"and Zeevi, A","cited_arxiv_id":null,"evidence_quote":"The linear-response bandit analysis whose peeling and margin techniques are adapted for the final regret summation over unbounded contexts."}],"review_version":1}