Decitabine and Talazoparib in Untreated AML and R/R AML

Inclusion Criteria: 1. Diagnosis of AML based on 2008 WHO criteria. AML may be de novo, following a prior hematologic disorder, including MDS or Philadelphia chromosome-negative myeloproliferative neoplasm, and/or therapy-related. 2. PHASES 1 AND 2: Patients with AML that has relapsed after, or is refractory to, first-line therapy, with or without subsequent additional therapy, and are currently considered unfit for, or unlikely to respond to, cytotoxic chemotherapy. 3. PHASE 2 ONLY: Patients previously untreated for AML who are considered unfit for cytotoxic chemotherapy by virtue of performance status, comorbidities, advanced age and/or low likelihood of response based on disease characteristics, or who decline cytotoxic induction chemotherapy. 4. Patients who have undergone autologous stem cell transplantation (autoSCT) are eligible provided that they are ≥ 4 weeks from stem cell infusion. 5. Patients who have undergone allogeneic SCT (alloSCT) are eligible if they are ≥ 60 days from stem cell infusion, have no evidence of graft versus host disease (GVHD) \> Grade 1, and are ≥ 2 weeks off all immunosuppressive therapy. 6. Previous cytotoxic chemotherapy must have been completed at least 3 weeks and radiotherapy at least 2 weeks prior to Day 1 of treatment on the study, and all adverse events (excluding alopecia) due to agents administered more than 4 weeks earlier should have recovered to \< Grade 1. Patients with hematologic malignancies are expected to have hematologic abnormalities at study entry. Hematologic abnormalities that are thought to be primarily related to leukemia are not considered to be toxicities (AE) and do not need to resolve to \< Grade 1. 7. Prior DNA methyl transferase inhibitor administration (azacitidine, decitabine, or guadecitabine) for AML or for antecedent MDS is allowed if this clinical trial is considered the best treatment option, but azacitidine, decitabine, or guadecitabine must have been stopped at least 3 weeks prior to Day 1 of treatment on the study. 8. All biologic agents including hematopoietic growth factors must have been stopped at least 1 week prior to Day 1 of treatment on the study. 9. Age ≥18 years. Because no dosing or adverse event data are currently available on the use of decitabine or talazoparib in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. 10. ECOG performance status ≤2 (Karnofsky ≥60%). 11. Life expectancy of greater than 2 months. 12. Patients must have normal organ and marrow function as defined below: * Total bilirubin within normal institutional limits unless thought due to hemolysis or to Gilbert's syndrome; * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal; * Creatinine within normal institutional limits; OR • Creatinine clearance ≥60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal. 13. Female patients of childbearing potential must have a negative pregnancy test, and female patients of childbearing potential and male patients must agree to use adequate contraception. Decitabine has been assigned to pregnancy category D by the FDA. Pregnant women must not take decitabine and female subjects must immediately stop taking decitabine and inform their doctor if they become pregnant during treatment. Decitabine is expected to result in adverse reproductive effects and can cause fetal harm when administered to a pregnant woman. In preclinical studies in mice and rats, decitabine was teratogenic, fetotoxic, and embryotoxic. Studies in pregnant animals to evaluate the effect of talazoparib on pregnancy have not been performed. Because decitabine is known to be teratogenic and the effects of talazoparib on the developing human fetus are unknown, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect that she is pregnant while she or her partner is participating in this study, she should inform the treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of decitabine and talazoparib administration. It is not known whether decitabine is excreted in human milk. Similarly, studies in lactating animals to evaluate the effect of talazoparib have not been performed, and thus, it is not known whether talazoparib is excreted in human milk. Therefore, breast-feeding should be stopped during decitabine and talazoparib treatment. 14. Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: 1. Patients with acute promyelocytic leukemia. 2. Patients with active central nervous system leukemia or requiring maintenance intrathecal chemotherapy. 3. Patients receiving concurrent chemotherapy, radiation therapy, or immunotherapy for AML. 4. Patients receiving any other investigational agents. 5. Hyperleukocytosis with \>50,000 blasts/μl. Hydroxyurea for blast count control is permitted before starting treatment, but must be stopped prior to starting treatment on the study. Patients will be withdrawn from the study if \> 50,000 blasts/μl occur or recur \> 14 days after starting treatment on the study. 6. Active, uncontrolled infection. Patients with infection controlled with antibiotics are eligible. 7. Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that per investigator's judgment would limit compliance with study requirements. 8. Patients who are pregnant or nursing. 9. Patients who have had chemotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) or radiotherapy within 2 weeks for antecedent malignancies prior to entering the study, or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. 10. History of allergic reactions attributed to compounds of similar chemical or biologic composition to decitabine or talazoparib. 11. Known HIV infection. HIV-positive patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. 12. Previous treatment with talazoparib.