{"id":"cb60d6ba-e4d7-42d4-87e6-123a94a57f78","arxiv_id":"2505.07594","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"The paper derives a finite-sample complexity bound for sampling Gaussian process dynamics and uses it to build a recursively feasible, safety-guaranteed model predictive controller.","lead":"The paper presents a way to guarantee safety of a controller when the system dynamics are learned from data using Gaussian processes. Instead of worst-case approximations, it samples many possible dynamics functions and proves a finite number suffices to capture the true system with high probability.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 1 is vacuous as stated for SE/Matérn kernels on R^n: the GP small-ball probability is zero, so φ(ε)=∞ and Eq. (7) gives no finite N.","rationale":"I read the paper as making a genuine finite-sample guarantee: for any ε>0 and 1−δ, N draws from the GP posterior contain, with probability ≥1−δ, one function uniformly ε-close to g*, and this sample underpins the reachable set, recursive feasibility, and safety/stability of the MPC. The Cameron-Martin shift, posterior-norm identity, Anderson inequality, and sample-retention argument are coherent, and I could not find an internal contradiction in Lemma 2, Lemma 3, or Theorem 3 beyond small presentational slips. The most load-bearing weakness I see is not the RKHS norm bound B_g, which is a standard and explicit assumption, but the domain over which the small-ball exponent is defined. Definition 1 and Theorem 1 use the supremum over R^n, while the cited small-ball rates and the numerical implementation concern compact domains. For SE and Matérn kernels on R^n, a stationary GP has unbounded sample paths a.s., so φ(ε)=∞ and the stated sample complexity collapses. This is a soundness issue for the central claim, but it is straightforwardly repairable by restricting all statements to a compact set Z containing the state-input constraint set or the reachable region; the proof structure then appears to survive. I therefore keep the reader's CONDITIONAL verdict, but for a different primary reason: the paper must add an explicit compact-domain assumption and use a certified (not Monte-Carlo) small-ball bound to make the finite-sample claim operative. The reader's identified concern about B_g is real and also deserves a caveat, but it is a standard assumption rather than a formal gap, so I regard the domain issue as more central.","tokens_in":21988,"tokens_out":30298,"duration_ms":291767,"concrete_test":"Analytically evaluate Pr(sup_{x∈R^n}|g(x)|<ε) for the zero-mean SE kernel used in the paper. If it is 0, as expected for a stationary GP with covariance decaying to 0, then Eq. (7) cannot yield a finite N and Theorem 1 is vacuous as written. Then repeat the calculation with the sup-norm restricted to the compact set Z=X×U (or the bounded region covered by the reachable sets); if the probability is positive and the proof of Eq. (7) goes through with finite φ(ε), the required repair is an explicit compact-domain assumption, and the remaining claims can be re-evaluated under that assumption.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Definition 1 and the norm in Section 2 define ∥g∥∞ = sup_{x∈R^n}|g(x)|. For the SE and Matérn kernels used in the paper, the zero-mean GP is stationary with covariance decaying to 0 at infinity; such Gaussian sample paths are unbounded on R^n almost surely (the supremum over [-r,r] grows like √(2 log r)). Hence Pr(∥g∥∞<ε)=0 for every ε>0, i.e., φ(ε)=∞. Plugging this into Eq. (7) gives p=0, log(1-p)=0, so N is not finite; the Corollary 1 rates N=O(e^{φ(ε)}) are likewise infinite. Theorem 1 therefore does not provide a finite N for the kernels it targets. Since Theorem 2 (reachable set), Theorem 3 (recursive feasibility and safety), and Theorem 4 (stability) all invoke Theorem 1, the central finite-sample guarantee is vacuous on the stated domain. The cited small-ball bounds [40] are for compact domains, and the numerical examples actually evaluate on a compact mesh, so the natural repair is to state the theory on a compact set Z (e.g., X×U or a bounded superset of the reachable set) and use the sup-norm over Z. This missing domain restriction is a correctness gap in the main claim, although it appears fixable without changing the proof structure. A secondary practical issue is that the simulations replace the certified φ(ε) by a Monte Carlo estimate, so the reported N does not carry the paper's 1−δ guarantee even after fixing the domain.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a finite-sample reachability and MPC framework for discrete-time nonlinear systems whose dynamics contain an unknown component g* modeled with Gaussian process regression. Theorem 1 gives a sample complexity bound N (Eq. (7)) such that, with probability at least 1-delta, at least one of N independent draws from the GP posterior is uniformly epsilon-close to g* in the sup norm; the proof combines a Cameron-Martin shift bound (Lemma 1) with a data-dependent constant C_D (Lemma 2) and a small-ball exponent phi(epsilon) (Definition 1). Theorem 2 extends this to a sampling-based reachable set that contains the true trajectory with high probability by propagating the residual epsilon-epistemic and aleatoric uncertainty with Lipschitz tubes. Building on this, the proposed sampling-based GP-MPC (Problem (16), Algorithm 1) is shown to be recursively feasible by removing falsified samples (Corollary 2, Theorem 3), and to yield an average-cost bound and practical asymptotic stability (Theorem 4). Two numerical examples illustrate the approach on a car lane-change maneuver and a pendulum stabilization task.","tokens_in":22245,"tokens_out":17150,"duration_ms":162216,"significance":"If the results are made fully correct, this is a valuable contribution to learning-based MPC. The core idea of treating epistemic uncertainty by sampling candidate dynamics and then retaining only those consistent with the observed trajectory is a natural way to avoid the conservatism of sequential robust propagation, and the recursive-feasibility mechanism for sampling-based MPC is of independent interest. The derivation is largely self-contained: the sample-complexity proof uses established small-ball, RKHS, and Cameron-Martin results, and the paper provides reproducible open-source code. The claimed finite-sample guarantees, if valid, would improve on scenario approaches that require the ground truth and the samples to share the same distribution. However, the current statement of Theorem 1 is not valid on the domain used in the paper, and the numerical implementation does not use the certified constants appearing in the theorem; these issues must be resolved before the central claims can be accepted.","major_comments":[{"comment":"The paper defines the Banach space B as functions g: R^n -> R with sup norm over the whole of R^n, and Definition 1 defines the small-ball exponent through Pr(||g||_infinity < epsilon) for g ~ GP(0,k). For the stationary squared-exponential and Matérn kernels used in the paper, a zero-mean Gaussian process on R^n has sample paths that are unbounded almost surely, so Pr(||g||_infinity < epsilon) = 0 for every epsilon > 0. Consequently phi(epsilon) = infinity, and Eq. (7) gives no finite N. This makes Theorem 1, and therefore Theorems 2-4 which invoke it, vacuous on the stated domain. The cited small-ball bounds in [40] are for compact domains, and the numerical examples indeed evaluate on compact grids, so the natural repair is to state all sup-norm statements over a compact set Z, e.g., X x U or a bounded superset of the reachable set, and to adapt Definition 1, Eq. (8), and Corollary 1 accordingly. This is a load-bearing correctness gap in the main claim, although it appears fixable without changing the proof structure.","section":"Section 2 (Notation) and Definition 1 / Theorem 1"},{"comment":"The definition of c_i in Eq. (19) is inconsistent with the proof of Lemma 3. In the proof, the one-step bound (20) gives ||x^n_{0|k+1} - x^n_{1|k}|| <= epsilon, and the recursion then yields c_i = L^i epsilon + 2||B_d||epsilon * sum_{j=0}^{i-1} L^j, where L^i is the i-th power of the Lipschitz constant. As printed, however, Eq. (19) uses the cumulative constant L_i defined before Theorem 2, which gives c_0 = 0 and would therefore remove the epsilon-close sample in the update rule (17), breaking Corollary 2 and Theorem 3. Please correct Eq. (19) and the surrounding notation so that the exponentiation is unambiguous and c_0 equals the correct one-step deviation bound.","section":"Section 5.2, Eq. (19) and Lemma 3"},{"comment":"The simulations do not use the certified small-ball exponent phi(epsilon) that appears in Theorem 1 and Corollary 1. Instead, the paper states that phi(epsilon) is 'empirically estimated' by evaluating how many GP posterior samples fall within an epsilon ball around the mean. Consequently, the numbers N reported in Figures 2-4 do not inherit the 1-delta guarantee of Theorem 1, and the sample-complexity rates in Corollary 1 are not what is actually used in the experiments. The authors should either compute phi(epsilon) via the certified upper bounds for the SE kernel on a compact domain, or explicitly present the numerical study as illustrative and not as a certified implementation of the theoretical guarantee.","section":"Section 6.1 (Implementation details) and Corollary 1"},{"comment":"The terminal ingredients are validated only on 100 newly sampled dynamics drawn around the upright position, while Assumptions 4 and 6 require the terminal set and terminal cost to satisfy invariance and the decrease condition for all n in N_0, i.e., for the N = 70 samples actually used in Problem (16). A common Lyapunov function found from 100 independent samples does not certify the property for the specific finite set N_0 used in the MPC. This is a gap between the theoretical assumptions and the numerical validation; please either verify Assumptions 4 and 6 on the actual sample set or state the weaker claim that the terminal ingredients are heuristically designed.","section":"Section 6.3 (Pendulum example) and Assumptions 4/6"}],"minor_comments":[{"comment":"The statement of Lemma 1 omits the square in the exponent: it should read e^{-(1/2)||h||_k^2}, since the proof and the subsequent use in Eq. (8) rely on the squared RKHS norm.","section":"Lemma 1"},{"comment":"The symbol epsilon is used both for the tolerance in Theorem 1 and for the tube radius epsilon := ||B_d||(epsilon + wbar). This overloaded notation is confusing when epsilon_k is defined as epsilon L_k; please use distinct symbols for the tolerance and the radius of the uncertainty ball.","section":"Section 4, Theorem 2"},{"comment":"The proof switches between the strict inequality ||g_n - g*||_infinity < epsilon in Eq. (8) and the non-strict inequality <= epsilon in Eq. (9). This is harmless but should be made consistent.","section":"Theorem 1, proof around Eq. (9)"},{"comment":"The formula for sqrt(beta_D) in Lemma 4 is missing a parenthesis around the log-determinant term; the intended expression is sqrt(beta_D) = B_g + sqrt(log det(I + lambda^{-2} K_D) + 2 log(2/delta)). Please clarify.","section":"Appendix A, Lemma 4"}],"recommendation":"major_revision","confidential_remarks":"The unbounded-domain issue is the most serious concern: it is not merely a presentation problem, because Theorem 1 as stated yields no finite N for the kernels used in the paper. The repair is straightforward (state the theory on a compact domain), and the rest of the proof structure appears sound, so I do not recommend rejection. However, the authors should also decide how to present the Monte Carlo estimate of phi(epsilon) in the experiments; currently the numerical claims outrun the certified theory. A revised version that fixes the domain, clarifies Eq. (19), and aligns the simulations with the certified constants would be suitable for reconsideration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. The paper has a genuinely new result — a finite-sample bound on how many GP posterior draws cover the unknown dynamics to tolerance ε — and a genuinely clever mechanism, falsified-sample removal, that gives recursive feasibility for sampling-based GP-MPC. But the main theorem as stated is vacuous for the kernels the paper actually uses. The sup-norm in Definition 1 is over all of R^n; for stationary kernels with decaying covariance (SE and Matérn), sample paths are unbounded on R^n almost surely, so the small-ball probability is zero for every ε, and Eq. (7) yields no finite N. The cited small-ball bounds [40] are for compact domains, so they don't rescue the statement. This is a real correctness gap in the headline claim, and it is easily fixed: state Theorem 1 and Corollary 1 on a compact set Z (for the closed-loop results, X×U works) with the sup-norm over Z, and the proofs go through unchanged. The numerics already live on a compact mesh.\n\nThe core machinery is otherwise sound. The Cameron–Martin shift, the C_D bound via GP confidence intervals, Anderson's inequality for the posterior small ball, and the tube propagation are all correct. The recursive-feasibility argument is the cleanest part: drop samples whose one-step predictions deviated beyond c_i, and the ε-close sample provably survives, so you lose nothing by shrinking the set. That genuinely extends the authors' earlier paper [35], which had neither finite-sample guarantees nor recursive feasibility. The comparison against robust GP-MPC [22] shows the conservatism gap clearly — the ellipsoids blow up around horizon 14 while the sampled tubes stay informative. Code is public.\n\nSoft spots, in proportion. The empirical estimation of the small-ball exponent in the simulations means the reported N values do not carry the 1−δ guarantee; the text discloses this but downplays it, and the experiments should label N as heuristic unless φ is certified. Assumption 1 (known RKHS norm bound B_g) is load-bearing and loose bounds make N prohibitive, but that is shared with the entire GP-confidence-bound literature. Presentation: Lemma 1's statement is missing the square on ||h||_k (the proof uses it), ε does double duty as tolerance and tube radius, and c_i is used in (17) before it is defined. Minor.\n\nThis is a paper for the safe-learning-and-control crowd; the sample-complexity bound also has independent interest for function-space sampling arguments. Send it to serious review. My call: referee it, and require the compact-domain fix plus an honest statement about N in the experiments. The contribution is real and the repair is small.","headline":"Solid new finite-sample GP-MPC paper with a clever recursive-feasibility mechanism, but Theorem 1 as stated is vacuous for SE/Matérn kernels over R^n until moved to a compact domain.","tokens_in":22846,"tokens_out":14778,"would_cite":true,"duration_ms":139826,"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":"This paper establishes that a finite number of GP-posterior dynamics samples suffices to build a provably safe, non-conservative reachable set, and that the resulting MPC is recursively feasible with high probability.","keywords":["Gaussian processes","model predictive control","reachable sets","sample complexity","small ball probability","safe control","uncertainty propagation","learning-based control"],"falsifier":"Take a known target $g^*$ inside the kernel's RKHS with $\\|g^*\\|_k \\le B_g$, compute $C_D$ exactly, estimate $\\phi(\\epsilon)$ by Monte Carlo, and repeatedly draw $N$ samples as in Eq. (7). If the empirical frequency with which at least one draw satisfies $\\|g_n - g^*\\|_\\infty < \\epsilon$ falls below $1-\\delta$ consistently, the bound in Theorem 1 is false.","tokens_in":21734,"feed_emoji":"🛡️","tokens_out":10988,"duration_ms":101192,"temperature":0.7,"pith_summary":"Model predictive control with Gaussian-process models currently faces a trade-off: approximation-based methods are tractable but lack safety guarantees, while worst-case robust methods are safe but overly conservative. This paper claims to resolve the trade-off by sampling a finite number of dynamics functions from the GP posterior: for any tolerance $\\epsilon>0$ and confidence $1-\\delta$, there is a finite sample count $N$ such that, with probability at least $1-\\delta$, one sampled function is uniformly $\\epsilon$-close to the unknown dynamics. With that sample in hand, the paper builds a reachable set that contains the true trajectory with high probability and designs a sampling-based MPC that is recursively feasible and satisfies state and input constraints with the same probability. The payoff is a safety certificate for nonlinear control that is neither heuristic nor hopelessly conservative.","feed_headline":"Finite GP samples are enough for safe, provable control","feed_subtitle":"A sample-count bound makes sampling-based MPC recursively feasible, with safety guaranteed at probability 1-delta.","key_machinery":"Three components carry the argument. The first is the small-ball probability of the prior GP, $\\Pr(\\|g\\|_\\infty < \\epsilon) = e^{-\\phi(\\epsilon)}$, which measures how often a random draw lands inside an $\\epsilon$-ball around the mean; known bounds for squared-exponential and Matérn kernels control $\\phi(\\epsilon)$. The second is a measure-shift lemma: shifting a centered GP by an RKHS function $h$ lowers the probability of any symmetric ball by no more than a factor $e^{-\\|h\\|_k^2/2}$, so the paper converts small-ball probabilities around the posterior mean into probabilities around the unknown $g^*$, using $C_D$ from Lemma 2 to bound $\\|g^* - \\mu\\|_{k_D}/2$. The third is the reachable-set construction: trajectories simulated from the $N$ sampled dynamics are inflated by balls of radius roughly $\\epsilon L^k$ (with $L$ the dynamics' Lipschitz constant), and a filtering rule $N_{k+1} = \\{n : \\|x^i_{n|k+1} - x^{i+1}_{n|k}\\| \\le c_i\\}$ removes samples falsified by the closed-loop data; retaining the $\\epsilon$-close sample is what makes recursive feasibility and the probability-$1-\\delta$ safety guarantee go through.","core_discovery":"The central result is a finite-sample coverage guarantee for GP dynamics models. Under the assumption that the unknown function $g^*$ belongs to the RKHS of the chosen kernel with known norm bound $B_g$, Theorem 1 states that drawing $N \\ge \\log(\\delta/2) / \\log(1 - e^{-(C_D + \\phi(\\epsilon))})$ independent functions from the GP posterior ensures that, with probability at least $1-\\delta$, at least one sample $g_n$ satisfies $\\|g_n - g^*\\|_\\infty < \\epsilon$, where $C_D$ is a data-dependent constant and $\\phi(\\epsilon)$ is the prior's small-ball exponent. The paper then propagates only the residual $\\epsilon$-epistemic uncertainty and bounded aleatoric noise through a Lipschitz tube to obtain a reachable set containing the true trajectory with probability $1-\\delta$ (Theorem 2). Building on this, the sampling-based GP-MPC optimizes over all sampled dynamics jointly, removes dynamics samples that are falsified by observed transitions, and thereby achieves recursive feasibility, closed-loop constraint satisfaction with probability $1-\\delta$ (Theorem 3), and practical asymptotic stability (Theorem 4).","pith_inferences":["A natural extension the paper leaves implicit is an adaptive stopping rule: sample dynamics sequentially and keep only those consistent with the observed transition tube; the required number of samples would then be data-dependent and potentially far smaller than the a priori $N$ of Eq. (7), though the probability argument would need a stopping-time correction.","The falsified-sample filtering rule is a generic recursive-feasibility mechanism for sampling-based MPC, so the same idea could be applied to ensemble or particle representations of uncertainty in finite-dimensional settings where scenario approaches currently give only a-posteriori guarantees.","The residual tube's radius grows like $L^k$, so for unstable dynamics ($L>1$) long horizons still incur exponential growth; pairing the samples with a local feedback law or a contraction metric, as the paper sketches in Remark 2, is likely to be necessary in practice, and the quantitative trade-off between feedback gain and sample count is not analyzed.","If the chosen kernel is misspecified and the true dynamics lies outside its RKHS, the entire $1-\\delta$ statement has no formal footing; a robustness margin on $B_g$ or a data-driven kernel selection step would be needed before the method could be deployed where the regularity assumption is doubtful."],"forward_implications":["A user can precompute a concrete sample budget $N$ from $\\epsilon$, $\\delta$, the kernel, and the data, so the safety guarantee does not rely on asymptotic arguments or post-hoc scenario validation.","Recursive feasibility means the probability-$1-\\delta$ constraint satisfaction holds at every closed-loop time step, not just for a single finite-horizon prediction.","Only the residual uncertainty (the tolerance $\\epsilon$ plus process noise) is propagated through the Lipschitz constant, so the reachable set avoids the exponential blow-up that sequential worst-case propagation produces in the robust GP-MPC baseline.","As $\\epsilon \\to 0$, the sample count grows like $(1/\\epsilon)^{C(\\log(1/\\epsilon))^d}$ for squared-exponential kernels and like $e^{C(1/\\epsilon)^{d/\\nu}}$ for Matérn kernels, which tells a practitioner how much additional computation buys a given improvement in tightness.","With positive definite costs, the closed loop is practically asymptotically stable: trajectories converge to a residual ball whose radius shrinks to zero as the process noise and $\\epsilon$ vanish jointly."],"supporting_citations":[{"why":"Supplies the high-probability GP confidence bounds that define the scaling factor $\\beta_D$ in the data-dependent constant $C_D$.","marker":"[7]"},{"why":"Provides the relation between prior and posterior RKHS norms used to compute $\\|g^* - \\mu\\|_{k_D}$ in Lemma 2.","marker":"[8]"},{"why":"States the RKHS regularity assumption (Assumption 1) that the unknown dynamics has a known RKHS-norm bound $B_g$.","marker":"[12]"},{"why":"Defines the small-ball exponent and gives the rates for squared-exponential and Matérn kernels used in Theorem 1 and Corollary 1.","marker":"[40]"},{"why":"Supplies Lemma 5.2, the measure-shift inequality that converts small-ball probabilities around the mean into probabilities around $g^*$.","marker":"[45]"},{"why":"Justifies Lemma 5, that the posterior small-ball probability dominates the prior small-ball probability.","marker":"[61]"},{"why":"The robust tube-based GP-MPC baseline whose sequential ellipsoid propagation the paper compares against and shows to be more conservative.","marker":"[22]"},{"why":"Prior numerical solver for sampling-based GP-MPC that the paper extends with finite-sample guarantees and recursive feasibility.","marker":"[35]"},{"why":"Provides the forward-sampling and re-conditioning technique used to simulate trajectories from the GP posterior in the algorithm.","marker":"[31]"}],"fun_headline_variants":["Finite GP samples suffice for safe MPC","Sampling-based GP-MPC with safety guarantees","Avoiding conservatism: finite-sample reachability","GP-MPC: recursive feasibility from sampled dynamics","Sample count bound enables safe GP control"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole guarantee hinges on the unknown dynamics actually belonging to the function space associated with the chosen kernel and having a known, usable size bound there; if that bound is wrong, too loose, or unavailable, the required sample count becomes meaningless or the claimed $1-\\delta$ safety no longer follows.","fun_headline_variants_meta":{"raw":{"variants":["Finite GP samples suffice for safe MPC","Sampling-based GP-MPC with safety guarantees","Avoiding conservatism: finite-sample reachability","GP-MPC: recursive feasibility from sampled dynamics","Sample count bound enables safe GP control"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000331,"raw_usage":{"total_tokens":1838,"prompt_tokens":935,"completion_tokens":903,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":551,"completion_tokens_details":{"reasoning_tokens":849}},"tokens_in":551,"tokens_out":903,"duration_ms":9095,"temperature":1.0,"reasoning_tokens":849,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:14:28.085327+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a known target $g^*$ inside the kernel's RKHS with $\\|g^*\\|_k \\le B_g$, compute $C_D$ exactly, estimate $\\phi(\\epsilon)$ by Monte Carlo, and repeatedly draw $N$ samples as in Eq. (7). If the empirical frequency with which at least one draw satisfies $\\|g_n - g^*\\|_\\infty < \\epsilon$ falls below $1-\\delta$ consistently, the bound in Theorem 1 is false.","supporting_citations":[{"cited_title":"Online learning for linearly parametrized control problems","cited_arxiv_id":null,"evidence_quote":"Supplies the high-probability GP confidence bounds that define the scaling factor $\\beta_D$ in the data-dependent constant $C_D$."},{"cited_title":"Information-theoretic regret bounds for gaussian process optimization in the bandit setting","cited_arxiv_id":null,"evidence_quote":"Provides the relation between prior and posterior RKHS norms used to compute $\\|g^* - \\mu\\|_{k_D}$ in Lemma 2."},{"cited_title":"Safe guaranteed exploration for non-linear systems","cited_arxiv_id":null,"evidence_quote":"States the RKHS regularity assumption (Assumption 1) that the unknown dynamics has a known RKHS-norm bound $B_g$."},{"cited_title":"The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities","cited_arxiv_id":null,"evidence_quote":"Justifies Lemma 5, that the posterior small-ball probability dominates the prior small-ball probability."},{"cited_title":"Learning-Based Model Predictive Control for Safe Exploration","cited_arxiv_id":null,"evidence_quote":"The robust tube-based GP-MPC baseline whose sequential ellipsoid propagation the paper compares against and shows to be more conservative."},{"cited_title":"Zeilinger","cited_arxiv_id":null,"evidence_quote":"Prior numerical solver for sampling-based GP-MPC that the paper extends with finite-sample guarantees and recursive feasibility."},{"cited_title":"Scenario-based Optimal Control for Gaussian Process State Space Models","cited_arxiv_id":null,"evidence_quote":"Provides the forward-sampling and re-conditioning technique used to simulate trajectories from the GP posterior in the algorithm."}],"review_version":1}