Study Assessing the Efficacy and Safety of Alpelisib + Nab-paclitaxel in Subjects With Advanced TNBC Who Carry Either a PIK3CA Mutation or Have PTEN Loss

Inclusion Criteria:

* Participant has histologically confirmed diagnosis of advanced (loco-regionally recurrent and not amenable to curative therapy), or metastatic (stage IV) TNBC
* Participant has either a measurable disease per RECIST 1.1 criteria or, if no measurable disease is present, then at least one predominantly lytic bone lesion or mixed lytic-blastic bone lesion with identifiable soft tissue component (that can be evaluated by CT/MRI) must be present. Part B1: Participants must have measurable disease
* Participant has adequate tumor tissue to identify the PIK3CA mutation status (either carrying a mutation or without a mutation) and the PTEN loss status; both of which will determine whether the subject can be allocated to Part A - PIK3CA mutation regardless of PTEN status; or to Part B1 - PTEN loss or to Part B2 - PTEN loss without a PIK3CA mutation
* Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Participant has received no more than one line of therapy for metastatic disease
* Participant has adequate bone marrow and organ function

Exclusion Criteria:

* Participant has received prior treatment with any PI3K, mTOR or AKT inhibitor
* Participant has a known hypersensitivity to alpelisib, nab-paclitaxel or to any of their excipients
* Participant has not recovered from all toxicities related to prior anticancer therapies to NCI CTCAE version 4.03 Grade ≤1; with the exception of alopecia
* Participant has central nervous system (CNS) involvement which was not previously treated and/or was newly detected at screening
* Participant with an established diagnosis of diabetes mellitus type I or uncontrolled type II based on Fasting Plasma Glucose and HbA1c
* Participant has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) based on investigator discretion
* Participant has a history of acute pancreatitis within 1 year prior to screening or past medical history of chronic pancreatitis
* Participant has currently documented pneumonitis/interstitial lung disease
* Participant has a history of severe cutaneous reactions, such as Steven-Johnson Syndrome (SJS), erythema multiforme (EM),Toxic Epidermal Necrolysis (TEN) or Drug Reaction with Eosinophilia and Systemic Syndrome (DRESS)
* Participant with unresolved osteonecrosis of the jaw