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CubicInterp found the stationary points of the interpolating cubic as -(c2 +- sqrt(c2^2 - 2 c1 c3)) / c3. For nearly quadratic data c3 is rounding noise and one of the two roots cancels: CubicInterp returned an end of the interval, or a point up to 28% off, instead of the minimiser. The roots are now -q / c3 and -2 c1 / q with q = c2 + sign(c2) sqrt(...).
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Jenkins Console Log Machine informationDistributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 52 bits physical, 57 bits virtual CPU(s): 192 On-line CPU(s) list: 0-191 Thread(s) per core: 2 Core(s) per socket: 48 Socket(s): 2 NUMA node(s): 2 Vendor ID: AuthenticAMD CPU family: 25 Model: 17 Model name: AMD EPYC 9474F 48-Core Processor Stepping: 1 Frequency boost: enabled CPU MHz: 1495.844 CPU max MHz: 4114.4229 CPU min MHz: 1500.0000 BogoMIPS: 7189.39 Virtualization: AMD-V L1d cache: 3 MiB L1i cache: 3 MiB L2 cache: 96 MiB L3 cache: 512 MiB NUMA node0 CPU(s): 0-47,96-143 NUMA node1 CPU(s): 48-95,144-191 Vulnerability Gather data sampling: Not affected Vulnerability Indirect target selection: Not affected Vulnerability Itlb multihit: Not affected Vulnerability L1tf: Not affected Vulnerability Mds: Not affected Vulnerability Meltdown: Not affected Vulnerability Mmio stale data: Not affected Vulnerability Old microcode: Not affected Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Not affected Vulnerability Spec rstack overflow: Mitigation; Safe RET Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; Enhanced / Automatic IBRS; IBPB conditional; STIBP always-on; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsa: Mitigation; Clear CPU buffers Vulnerability Tsx async abort: Not affected Vulnerability Vmscape: Mitigation; IBPB before exit to userspace Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good amd_lbr_v2 nopl xtopology nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba perfmon_v2 ibrs ibpb stibp ibrs_enhanced vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local user_shstk avx512_bf16 clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin cppc arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif x2avic v_spec_ctrl vnmi avx512vbmi umip pku ospke avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg avx512_vpopcntdq la57 rdpid overflow_recov succor smca fsrm flush_l1d debug_swap G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin |
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Your test relies on |
The existing test relies on c3 being rounding noise, whose value FMA contraction or another compiler can change. Data from -x + x^2 at x1 = 1 make every coefficient exact and c3 = 0 on any platform; develop returned the lower bound there, since the root was 0 / 0.
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Fair point, added. Data from One more note, on the other degenerate cases: with |
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Jenkins Console Log Machine informationDistributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 43 bits physical, 48 bits virtual CPU(s): 256 On-line CPU(s) list: 0-255 Thread(s) per core: 2 Core(s) per socket: 64 Socket(s): 2 NUMA node(s): 2 Vendor ID: AuthenticAMD CPU family: 23 Model: 49 Model name: AMD EPYC 7742 64-Core Processor Stepping: 0 Frequency boost: enabled CPU MHz: 1494.281 CPU max MHz: 3416.0681 CPU min MHz: 1500.0000 BogoMIPS: 4491.85 Virtualization: AMD-V L1d cache: 4 MiB L1i cache: 4 MiB L2 cache: 64 MiB L3 cache: 512 MiB NUMA node0 CPU(s): 0-63,128-191 NUMA node1 CPU(s): 64-127,192-255 Vulnerability Gather data sampling: Not affected Vulnerability Indirect target selection: Not affected Vulnerability Itlb multihit: Not affected Vulnerability L1tf: Not affected Vulnerability Mds: Not affected Vulnerability Meltdown: Not affected Vulnerability Mmio stale data: Not affected Vulnerability Old microcode: Not affected Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Mitigation; untrained return thunk; SMT enabled with STIBP protection Vulnerability Spec rstack overflow: Mitigation; Safe RET Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; Retpolines; IBPB conditional; STIBP always-on; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsa: Not affected Vulnerability Tsx async abort: Not affected Vulnerability Vmscape: Mitigation; IBPB before exit to userspace Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl xtopology nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip rdpid overflow_recov succor smca sev sev_es G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin |
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A relatively minor numerics improvement.
AI use disclosure: This was developed with the help of Claude Code (Opus 5.5, model ID claude-opus-5-5).
Submission Checklist
./runTests.py src/test/unitmake cpplintSummary
CubicInterp(src/stan/optimization/bfgs_linesearch.hpp) minimises the cubicWhen the data are (nearly) quadratic,$c_3$ is rounding noise. For $c_2 > 0$ the numerator of $s_2$ then cancels, and $s_2$ , the minimiser $\approx -c_1/c_2$ , came out anywhere: $10^{-12}$ instead of 0.1 for data from $\phi(x) = -x + x^2/0.2$ at $x_1 = 1$ ), or a point up to 28% off (0.128 at $x_1 = 0.4$ ). The roots are now computed as
CubicInterpreturned an end of the interval (the same two roots ($s_1 s_2 = 2 c_1 / c_3$ ), with no subtraction of nearly equal numbers. As $c_3 \to 0$ , $s_1$ goes to $\pm\infty$ (outside the interval) and $s_2$ to $-c_1/c_2$ .
BFGSMinimizer::stepusesCubicInterpfor the first trial step of every iteration after the first (except after a reset): 1.01 times the minimiser of the cubic along the previous step overIntended Effect
CubicInterpreturns the minimiser of the interpolating cubic for any data, including nearly quadratic data (typical near the optimum), where it returned an end of the interval or a point up to 28% off.BFGSMinimizeruses it for the first trial step of most iterations, so that step is again the cubic's estimate. When it was the lower end,How to Verify
OptimizationBfgsLinesearch.CubicInterp_quadratic_data(src/test/unit/optimization/bfgs_linesearch_test.cpp): data at 0 andCubicInterpandCubicInterp_6arginbfgs_linesearch_test.cpp,bfgs_minimizer_test.cpp,bfgs_test.cpp,bfgs_exponential_boundary_test.cpp,services/optimize/{bfgs,lbfgs,bfgs_jacobian,lbfgs_jacobian}_test.cppand the Pathfinder testsservices/pathfinder/{eight_schools,normal_glm}_test.cpp.Side Effects
In-process A/B harness against develop (gradient evaluation counts, platform independent); I can share it. Behaviour changes:
tol_rel_obj = tol_rel_grad = 1, where runs end at the precision limit and small changes decide where they stop, some configurations need more evaluations (up to 1.20 times develop's for L-BFGS on a negative binomial regression, 1.15 for dense BFGS on a Laplace GP) and others fewer (down to 0.77).Documentation
None.
Copyright and Licensing
Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company):
Jáchym Barvínek jachymb@gmail.com
By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses: