OPINION

Petitioners Lonnie Peek, Louis Moon, and Deven Suesue are statutorily eligible for early release from prison in exchange for the successful completion of a residential drug abuse treatment program (“RDAP”). The Bureau of Prisons (“BOP”), however, has enacted a regulation disqualifying them from the early release incentive on the basis of their current convictions for felon in possession and one petitioner’s past conviction for robbery. See 28 C.F.R. § 550.55 (b). Petitioners each filed for a writ of habeas corpus asking the district court to invalidate the regulation under § 706 of the Administrative Procedure Act (“APA”). The district court dismissed the petitions, and the appeals were consolidated. We have jurisdiction under 28 U.S.C. § 1291 and § 2253 and we affirm.

I. FACTS AND PROCEDURAL BACKGROUND

Petitioners were each convicted of being a felon in possession of a firearm under 18 U.S.C. § 922 (g), and are either currently serving sentences in BOP facilities or serving terms of supervised release. At the time of his conviction, Petitioner Moon had a past conviction for robbery, but he received no criminal history points under the Sentencing Guidelines because the conviction was more than 15 years old.

In 1990, Congress directed the BOP to create programs to treat substance abuse among inmates. See 18 U.S.C. § 3621 (b). To encourage participation in this pro gram, Congress subsequently determined that inmates who successfully complete the program would be eligible for up to one year of early release from prison — as long as the inmate had been convicted of a “nonviolent offense.” Id. § 3621(e)(2)(B).

Under the authority delegated by this statute, the BOP has implemented a regulation that categorically excludes certain classes of inmates from eligibility for § 3621(e)’s early release incentive. See 28 C.F.R. § 550.55 (b). Petitioners challenge two aspects of this regulation: first, the exclusion of inmates convicted of “[a]n offense that involved the ... possession ... of a firearm,” id. § 550.55(b)(5)(ii); and second, the exclusion of inmates who have a prior conviction for homicide, forcible rape, robbery, aggravated assault, arson, kidnapping, or child sexual abuse, regardless of the age of that conviction, id. § 550.55(b)(4).

The history of the BOP’s attempts to implement these categorical exclusions is lengthy but relevant. Initially, the regulation defined the term “nonviolent offense” in § 3621(e) with reference to the statutory definition of “crime of violence” found in 18 U.S.C. § 924 (c)(3). See 28 C.F.R. § 550.58 (1995). We invalidated that regulation, holding that the inclusion of a § 922(g) possession charge is not a reasonable interpretation of the term “crime of violence” in § 924(c)(3). Davis v. Crabtree, 109 F.3d 566, 569 (9th Cir.1997). This eventually created a circuit split.

To resolve this circuit split, the BOP dropped the reference to § 924(c)(3) and instead asserted its discretionary authority to determine eligibility for early release under § 3621(e). In 1997, the BOP published an interim rule, effective immediately, that categorically excluded from eligibility for early release inmates with current convictions for felony offenses “involv[ing] the carrying, possession, or use of a firearm.” 28 C.F.R. § 550.58 (a)(l)(vi) (1998). In addition, the regulation continued to exclude prisoners with prior convictions for certain offenses. Id. § 550.58(a)(l)(iv).

We upheld the Bureau’s authority to so disqualify otherwise statutorily eligible inmates. See Bowen v. Hood, 202 F.3d 1211, 1220 (9th Cir.2000) (holding that the 1997 rule’s exclusion based on firearms possession was a reasonable exercise of discretion granted by the statute); Jacks v. Crabtree, 114 F.3d 983, 986 (9th Cir. 1997) (holding that the 1995 rule’s exclusion of inmates with prior convictions for certain offenses was entitled to deference and was reasonable). The Supreme Court later agreed, holding that “the agency’s interpretation is reasonable both in taking account of preconviction conduct and in making categorical exclusions.” Lopez v. Davis, 531 U.S. 230, 242 , 121 S.Ct. 714 , 148 L.Ed.2d 635 (2001). The Court explained that “the Bureau need not blind itself to preconviction conduct that the agency reasonably views as jeopardizing life and limb. By denying eligibility to violent offenders, the statute manifests congressional concern for preconviction behavior — and for the very conduct leading to conviction.” Id. The Court also found that “[t]he Bureau reasonably concluded that an inmate’s prior involvement with firearms, in connection with the commission of a felony, suggests his readiness to resort to life-endangering violence and therefore appropriately determines the early release decision.” Id. at 244 , 121 S.Ct. 714 .

The Lopez Court declined to reach the question of whether the BOP had complied with the notice-and-eomment provisions of the APA in promulgating the 1997 rule. Id. at 244 n. 6, 121 S.Ct. 714 . We took up this question in Paulsen v. Daniels, holding that the BOP had violated the APA by “implementing] a rule first, and then seeking] comment later.” 413 F.3d 999 , 1005 (9th Cir.2005). We invalidated the 1997 interim rule, declined to reinstate the 1995 version because it was also invalid, and noted that the law currently in effect was a final rule that had been promulgated in 2000. Id. at 1008.

The 2000 rule finalized the 1997 interim rule without change. Id. at 1003; see 28 C.F.R. § 550.58 (2001). Once again, we invalidated the BOP’s efforts. In Arrington v. Daniels, we held that the 2000 rule, insofar as it categorically excluded inmates convicted of firearm-possession offenses, was arbitrary and capricious under § 706(2)(A) of the APA because the agency failed to give a reasoned basis for its action. 516 F.3d 1106, 1113-14 (9th Cir.2008). In Arrington, we found that the administrative record did not contain the rationale advanced by the agency during litigation, id. at 1113 , and concluded that the BOP had “failed to set forth a rationale for its decision to categorically exclude prisoners convicted of offenses involving the carrying, possession, or use of firearms from eligibility for a sentence reduction under § 3621(e),” id. at 1114.

Following Arrington, we invalidated the exclusion based on prior convictions in Crickon v. Thomas, 579 F.3d 978 (9th Cir.2009). Crickon noted that “[o]ur recent ruling in Arrington squarely controls the outcome of the present case,” id. at 983 , and once again criticized the BOP for enacting a regulation without articulating a supporting rationale, id. at 984-85 .

Not to be deterred, the BOP responded to Arrington and Crickon by enacting identical provisions in a 2009 rule. See 28 C.F.R. § 550.55 . It is this rule that Petitioners here challenge—specifically, the exclusions set forth in 28 C.F.R. § 550.55 (b)(5)(h) and § 550.55(b)(4). At the outset, we note that every other circuit court to consider the issue has held either the current or prior version of this regulation to be valid under the APA. See Licon v. Ledezma, 638 F.3d 1303, 1311 (10th Cir.2011); Giannini v. Fed. Bureau of Prisons, 405 Fed.Appx. 96, 97 (8th Cir.2010); Stevenson v. FCI Waseca, 383 Fed.Appx. 587, 588 (8th Cir.2010); Handley v. Chapman, 587 F.3d 273, 282 (5th Cir.2009); Gardner v. Grandolsky, 585 F.3d 786, 791-92 (3d Cir.2009); Gatewood v. Outlaw, 560 F.3d 843, 848-49 (8th Cir.2009).

The district court issued three separate opinions, each finding that the BOP’s regulation is valid under APA § 706. Petitioners timely appealed. Petitioners argue that: (1) the articulated rationale is once again insufficient to justify the rule; (2) a heightened APA standard should apply to rules that involve the loss of liberty; (3) the legal error in the accompanying Program Statement infects the regulation and renders it invalid; (4) the BOP was required to reach a decision on the basis of available statistics rather than merely invoking its experience; and (5) the BOP’s interpretation conflicts with Congress’ expressed intent. In response, the BOP argues that it has cured the defects identified in Arrington and Crickon , and that the public safety rationale justifies the regulation.

II. DISCUSSION

A. The BOP Satisfied § 706 of the APA by Articulating a Public Safety Rationale.

Section 706 of the APA grants authority to a reviewing court to “hold unlawful and set aside agency action, findings, and conclusions found to be ... arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with law.” 5 U.S.C. § 706 (2)(A). “The scope of review under the ‘arbitrary and capricious’ standard is narrow and a court is not to substitute its judgment for that of the agency.” Motor Vehicle Mfrs. Ass’n v. State Farm Mut. Auto. Ins. Co., 463 U.S. 29, 43 , 103 S.Ct. 2856 , 77 L.Ed.2d 443 (1983). Agency action is presumed to be valid and must be upheld if a reasonable basis exists for the agency decision. Sacora v. Thomas, 628 F.3d 1059, 1068 (9th Cir.2010) (citing Crickon, 579 F.3d at 982 ). “A reasonable basis exists where the agency considered the relevant factors and articulated a rational connection between the facts found and the choices made.” Arrington, 516 F.3d at 1112 (internal quotation marks omitted).

The district court correctly found that, in enacting the categorical exclusions at issue in this case, the agency offered a public safety rationale in the administrative record. The BOP argues that this cures the procedural defects identified by the Arrington and Crickon courts. Petitioners argue that, while it is true that we previously invalidated the regulation for the failure to offer any contemporaneous rationale, it is not true that the present regulation’s rationale cured that procedural defect. We uphold the regulation.

1. The Bureau Did Not Violate the APA in Enacting 28 C.F.R. § 550.55 (b)(5)(h).

When enacting the 2009 regulation, the Bureau stated:

Drug Abuse Treatment Program: Subpart Revision and Clarification and Eligibility of D.C. Code Felony Offenders for Early Release Consideration, 74 Fed.Reg. 1892, 1895 (Bureau of Prisons Jan. 14, 2009).

The defect identified in Arrington — a failure to articulate any supporting rationale in the administrative record, 516 F.3d at 1113 — has been cured here. The Bureau clearly stated that, “in the correctional experience of the Bureau, the offense conduct of both armed offenders and certain recidivists suggests that they pose a particular risk to the public.” 74 Fed.Reg. at 1895. The Bureau further explained that it was exercising its discretion because “[t]here is a significant potential for violence from criminals who carry, possess or use firearms” and that “in committing such offenses, these inmates displayed a readiness to endanger another’s life.” Id. Although the Bureau could have proffered a fuller explanation, the APA does not demand more.

2. The Bureau did not violate the APA in enacting 28 C.F.R. § 550.55 (b)(4).

With regard to the exclusion based on prior convictions in § 550.55(b)(4), the BOP explained:

74 Fed.Reg. at 1894.

We had previously criticized this portion of the BOP’s regulation because, “[bjeyond explaining that it decided upon the four identified categories of convictions because of the variation in violence level that may be found in state convictions, the BOP provided no explanation for its decision to look to prior convictions as the appropriate basis to determine categorical exclusions.” Crickon, 579 F.3d at 984 (citation omitted). This time, the BOP has explained, minimally, that “commission of such offenses [homicide, forcible rape, robbery, aggravated assault, arson, and kidnaping] rationally reflects the view that such inmates displayed readiness to endanger the public.” 74 Fed.Reg. at 1894. As we and the Supreme Court have found, this reasoning is permissible and based on common sense. Lopez, 531 U.S. at 242 , 121 S.Ct. 714 ; Jacks, 114 F.3d at 985-86 . Now that the agency has explicitly relied on such reasoning in the administrative record, we see no reason to overturn the regulation. Nor does the lack of a temporal restriction on prior convictions invalidate the regulation: implicit in the Bureau’s reasoning is the determination that a prior conviction for any of these offenses, no matter its age, “rationally reflects the view that such inmates displayed readiness to endanger the public.” 74 Fed.Reg. at 1894.

Petitioners argue that this rationale is insufficient because it relies on erroneous facts. The BOP stated that it chose the particular crimes “as identified in the FBI’s Uniform Crime Reporting Program (UCR).” Id. The Bureau then explained that “[t]he definitions of these terms were developed for the National Incident-Based Reporting System and are identified in the UCR due to their inherently violent nature and particular dangerousness to the public.” Id. Petitioners point out, however, that the crimes were actually identified in the UCR because they are “serious crimes, they occur with regularity in all areas of the country, and they are likely to be reported to the police.” Fed. Bureau of Investigation, Uniform Crime Report, Crime in the United States, 2009, at 1 (Sept. 2010), http://www2.fbi.gov/ucr/cius 2009/documents/09offensedefinitions.pdf.

The Petitioners’ argument misses the mark. First, it is not clear that “seriousness” is a significantly different measure from “violent nature” and “dangerous ness.” The agency is entitled to rely on an existing index of serious crimes to identify crimes that are dangerous. Second, the BOP never states that it chose these crimes because they were listed in the UCR as dangerous and violent. Instead, it states that: (1) these crimes are listed in the UCR as dangerous and violent, and (2) the commission of these crimes “rationally reflects the view that such inmates displayed readiness to endanger the public.” 74 Fed.Reg. at 1894. Because the agency is entitled to reach the latter determination, the regulation is valid under the APA.

B. This Case Does Not Call for Application of a Heightened APA Standard, If Any Exists.

Petitioners argue that “[t]his case calls for more scrupulous application of the State Farm standard in light of’ the fact that it “involves human freedom,” whereas “[t]he State Farm standard for application of § 706 of the APA evolved through cases involving standard areas of administrative regulation, such as auto safety, pollution control, and financial transactions.”

Petitioners cite no case that has ever adopted this proposition. Furthermore, even if “loss of liberty” were to be reviewed under a hypothetically heightened standard, such a standard would not be applicable to this case. An inmate has no liberty interest in a sentence reduction in exchange for completion of RDAP. McLean v. Crabtree, 173 F.3d 1176, 1184-85 (9th Cir.1999) (“[D]enial merely means that the inmate will have to serve out his sentence as expected.” (quoting Jacks, 114 F.3d at 986 n. 4)). If there is no liberty interest in the reduction, then a denial of eligibility for that reduction cannot affect an inmate’s liberty interest.

Petitioners also argue that the BOP’s “history of violating the APA” should be taken into account when applying the State Farm standard. But the BOP’s unsuccessful attempts to enact the regulation at issue do not demonstrate willful non-compliance with statutory mandates, and no court has ever found this to be case.

C. The Legal Error in the Accompanying Program Statement Does Not Render the Regulation Invalid.

Petitioners note that in the Program Statement accompanying the 2009 rule, the BOP continued to define a felon-in-possession crime under 18 U.S.C. § 922 (g) as a crime of violence. See Program Statement No. 5162.05, at 3-A (Bureau of Prisons Mar. 16, 2009), available at www.bop.gov/pohcy/progstaV5162_005.pdf. This is in conflict with our pronouncement to the contrary in Davis, 109 F.3d at 569 . However, Petitioners point to nothing in the administrative record indicating that the BOP relied on its categorization of § 922(g) as a “crime of violence” when reaching its decision to adopt § 550.55(b)(5)(h). Instead, Petitioners shift the burden to the agency to affirmatively demonstrate that it has not relied on this legal error in enacting § 550.55(b)(5)(h), by arguing that “the BOP failed to establish that the legal error did not taint the exercise of discretion in the parallel program statement.” It does not make sense to require an agency to state all of the reasons for which it did not reach a decision, and Petitioners have not directed us to any authority supporting the proposition that this burden is on the agency. Because Petitioners have not identified any evidence in the record showing that in promulgating § 550.55(b)(5)(h) the BOP relied on the proposition that a violation of § 922(g) is categorically a crime of violence under § 924(c)(3), they have not shown that the regulation is infected by the legal error contained in the program statement.

D. The BOP Was Not Required to Reach a Decision on the Basis of Statistics or Other Empirical Evidence.

Petitioners argue that, in light of the “read[y] availability]” of relevant “empirical data or studies,” the BOP’s decision not to collect and consider any of that evidence invalidates the regulation. Petitioners contend that the regulation fails to comply with the “clear road map” that “list[s] the missing agency actions needed for compliance with the APA” which we gave in Crickon .

In Crickon , we stated:

579 F.3d at 985 . The flaw in Petitioners’ reasoning is that Crickon did not indicate that these actions are necessary for an agency’s compliance with the APA; it merely listed several actions which would have been sufficient for APA compliance. Crickon does not support Petitioners’ argument that the BOP was required to develop and rely on detailed statistics before promulgating this rule.

In Sacora v. Thomas, we noted that “[t]he BOP ... is entitled to use its experience in interpreting and administering a statute.” 628 F.3d at 1067 . We held that, although “[i]t may have been preferable for the BOP to support its conclusions with empirical research,” “it was reasonable for the BOP to rely on its experience, even without having quantified it in the form of a study.” Id. at 1069 . Petitioners distinguish Sacora because the rule at issue in that case limited half-way house placement to six months, and the agency did not have “a large trove of untapped ... data” concerning the proposed change, whereas in this case, the BOP has many years of statistics based on its past efforts to categorically exclude certain prisoners from the early release incentive. This distinction is unpersuasive. Sacora made no mention of whether it would have been feasible for the BOP to gather data related to halfway house placement, and no indication that this consideration was a factor in the decision. We follow Sacora and hold that the BOP is entitled to invoke its experience as a justification for the present rule.

E. The BOP’s Interpretation Does Not Conflict with Congress’ Expressed Intent.

Petitioners argue that narrowing of the categories of statutorily eligible inmates is inconsistent with Congress’ intent to “maximize the early release incentive and to reduce the prison population.” Although it is true that our decision in Crick-on criticized the BOP for enacting a regulation that was “difficult to square with Congress’s expressed intent to provide an incentive to encourage maximum participation in the BOP’s substance abuse treatment programs,” 579 F.3d at 986 , the idea that the regulation should be struck down solely because of perceived inconsistencies with congressional intent, as distinct from congressional command, is in tension with the Supreme Court’s ruling in Lopez. See 531 U.S. at 242 , 121 S.Ct. 714 (“[A]ll we must decide is whether the Bureau, the agency empowered to administer the early release program, has filled the statutory gap in a way that is reasonable in light of the legislature’s revealed design. We think the agency’s interpretation is reasonable both in taking account of pre conviction conduct and in making categorical exclusions.” (citations omitted) (internal quotation marks omitted)).

Furthermore, the administrative record reflects the fact that the Bureau has had some difficulty in accommodating all of the inmates who wish to participate in RDAP:

74 Fed.Reg. at 1893. It would be unreasonable to criticize the Bureau for failing to maximize inmate participation when the Bureau is already struggling with its limited resources to accommodate all of the inmates who currently do wish to participate. It is clear to us that the agency is entitled to take a categorical approach to solving this problem.

III. CONCLUSION

We join our sister circuits in holding that the Bureau has not violated the APA in excluding inmates from consideration for early release who have a current conviction for felon in possession or a past conviction for homicide, forcible rape, robbery, aggravated assault, arson, kidnapping, or child sexual abuse.

AFFIRMED.

. Although two of the three petitioners are currently serving terms of supervised release, "relief may still be available in the form of modification, amendment, or termination of their supervised release.” Arrington v. Daniels, 516 F.3d 1106 , 1111 n. 4 (9th Cir.2008) (citing 18 U.S.C. § 3583 (e)(2)); see also Paul sen v. Daniels, 413 F.3d 999 , 1005 n. 3 (9th Cir.2005). Here, because the petitioners completed RDAP while in prison, a decision invalidating the regulation rendering them ineligible for early release in exchange for completing RDAP could provide a basis to shorten their terms of supervised release. . The Eighth, Tenth, and Eleventh Circuits agreed that the regulation adopted an unreasonable definition of "crime of violence,” see Martin v. Gerlinski, 133 F.3d 1076 , 1079 (8th Cir.1998); Fristoe v. Thompson, 144 F.3d 627, 631 (10th Cir.1998); Byrd v. Hasty, 142 F.3d 1395, 1398 (11th Cir.1998), but the Fourth and Fifth Circuits held otherwise, see Pelissero v. Thompson, 170 F.3d 442, 447 (4th Cir.1999); Venegas v. Henman, 126 F.3d 760, 763 (5th Cir.1997). . We review a district court’s dismissal of a petition for writ of habeas corpus de novo. Bowen, 202 F.3d at 1218 .